IXL skill plan | Geometry plan for EngageNY Math

Skill plan for EngageNY Math - Geometry

IXL provides skill alignments with recommended IXL skills for each module. Find the IXL skills that are right for you below!

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1	Module 1 Congruence, Proof, and Constructions
Topic A - Basic Constructions
Lessons 1 & 2: Construct an Equilateral Triangle		1. Lines, line segments, and rays 2. Construct an equilateral triangle or regular hexagon Also consider: • Construct a congruent segment • Construct an equilateral triangle inscribed in a circle • Construct a regular hexagon inscribed in a circle
Lessons 1 & 2: Construct an Equilateral Triangle
1. Lines, line segments, and rays 2. Construct an equilateral triangle or regular hexagon Also consider: • Construct a congruent segment • Construct an equilateral triangle inscribed in a circle • Construct a regular hexagon inscribed in a circle

Lesson 3: Copy and Bisect an Angle		1. Construct an angle bisector 2. Construct a congruent angle Also consider: • Angle vocabulary • Angle bisectors
Lesson 3: Copy and Bisect an Angle
1. Construct an angle bisector 2. Construct a congruent angle Also consider: • Angle vocabulary • Angle bisectors

Lesson 4: Construct a Perpendicular Bisector		1. Construct the midpoint or perpendicular bisector of a segment Also consider: • Construct a perpendicular line
Lesson 4: Construct a Perpendicular Bisector
1. Construct the midpoint or perpendicular bisector of a segment Also consider: • Construct a perpendicular line

Lesson 5: Points of Concurrencies		1. Construct the circumcenter or incenter of a triangle 2. Construct the inscribed or circumscribed circle of a triangle
Lesson 5: Points of Concurrencies
1. Construct the circumcenter or incenter of a triangle 2. Construct the inscribed or circumscribed circle of a triangle

Checkpoint opportunity		1. Checkpoint: Definitions of geometric objects
Checkpoint opportunity
1. Checkpoint: Definitions of geometric objects
Topic B - Unknown Angles
Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point		1. Find measures of complementary, supplementary, vertical, and adjacent angles 2. Angle diagrams: solve for the variable Also consider: • Identify complementary, supplementary, vertical, adjacent, and congruent angles
Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point
1. Find measures of complementary, supplementary, vertical, and adjacent angles 2. Angle diagrams: solve for the variable Also consider: • Identify complementary, supplementary, vertical, adjacent, and congruent angles

Lesson 7: Solve for Unknown Angles—Transversals		1. Transversals of parallel lines: find angle measures 2. Transversals of parallel lines: solve for x Also consider: • Transversals: name angle pairs
Lesson 7: Solve for Unknown Angles—Transversals
1. Transversals of parallel lines: find angle measures 2. Transversals of parallel lines: solve for x Also consider: • Transversals: name angle pairs

Lesson 8: Solve for Unknown Angles—Angles in a Triangle		1. Triangle Angle-Sum Theorem 2. Exterior Angle Theorem 3. Congruency in isosceles and equilateral triangles Also consider: • Classify triangles
Lesson 8: Solve for Unknown Angles—Angles in a Triangle
1. Triangle Angle-Sum Theorem 2. Exterior Angle Theorem 3. Congruency in isosceles and equilateral triangles Also consider: • Classify triangles

Lesson 9: Unknown Angle Proofs—Writing Proofs Lesson 10: Unknown Angle Proofs—Proofs with Constructions Lesson 11: Unknown Angle Proofs—Proofs of Known Facts		1. Proofs involving angles 2. Proofs involving parallel lines I 3. Proofs involving triangles I
Lesson 9: Unknown Angle Proofs—Writing Proofs Lesson 10: Unknown Angle Proofs—Proofs with Constructions Lesson 11: Unknown Angle Proofs—Proofs of Known Facts
1. Proofs involving angles 2. Proofs involving parallel lines I 3. Proofs involving triangles I
Topic C - Transformations/Rigid Motions
Lesson 12: Transformations—The Next Level		1. Reflection, rotation, and translation
Lesson 12: Transformations—The Next Level
1. Reflection, rotation, and translation

Lesson 13: Rotations		1. Rotate polygons about a point Also consider: • Rotations: graph the image
Lesson 13: Rotations
1. Rotate polygons about a point Also consider: • Rotations: graph the image

Lesson 14: Reflections		1. Reflections: graph the image
Lesson 14: Reflections
1. Reflections: graph the image

Lesson 15: Rotations, Reflections, and Symmetry		1. Count lines of symmetry 2. Draw lines of symmetry Also consider: • Line symmetry • Rotational symmetry
Lesson 15: Rotations, Reflections, and Symmetry
1. Count lines of symmetry 2. Draw lines of symmetry Also consider: • Line symmetry • Rotational symmetry

Lesson 16: Translations		1. Translations: graph the image Also consider: • Construct parallel lines
Lesson 16: Translations
1. Translations: graph the image Also consider: • Construct parallel lines

Lesson 17: Characterize Points on a Perpendicular Bisector		1. Perpendicular Bisector Theorem
Lesson 17: Characterize Points on a Perpendicular Bisector
1. Perpendicular Bisector Theorem

Lesson 18: Looking More Closely at Parallel Lines		1. Proofs involving parallel lines II
Lesson 18: Looking More Closely at Parallel Lines
1. Proofs involving parallel lines II

Lesson 19: Construct and Apply a Sequence of Rigid Motions		1. Transformations that carry a polygon onto itself Also consider: • Sequences of congruence transformations: graph the image • Congruence transformations: mixed review
Lesson 19: Construct and Apply a Sequence of Rigid Motions
1. Transformations that carry a polygon onto itself Also consider: • Sequences of congruence transformations: graph the image • Congruence transformations: mixed review

Lesson 20: Applications of Congruence in Terms of Rigid Motions		1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures
Lesson 20: Applications of Congruence in Terms of Rigid Motions
1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures

Lesson 21: Correspondence and Transformations		1. Prove triangles are congruent using rigid motions 2. Sequences of congruence transformations: find the rules 3. Determine if two figures are congruent: justify your answer
Lesson 21: Correspondence and Transformations
1. Prove triangles are congruent using rigid motions 2. Sequences of congruence transformations: find the rules 3. Determine if two figures are congruent: justify your answer

Checkpoint opportunity		1. Checkpoint: Line and angle theorems
Checkpoint opportunity
1. Checkpoint: Line and angle theorems
Topic D - Congruence
Lesson 22: Congruence Criteria for Triangles—SAS Lesson 23: Base Angles of Isosceles Triangles		1. Proofs involving SAS
Lesson 22: Congruence Criteria for Triangles—SAS Lesson 23: Base Angles of Isosceles Triangles
1. Proofs involving SAS

Lesson 24: Congruence Criteria for Triangles—ASA and SSS		1. Proofs involving ASA 2. Proofs involving SSS
Lesson 24: Congruence Criteria for Triangles—ASA and SSS
1. Proofs involving ASA 2. Proofs involving SSS

Lesson 25: Congruence Criteria for Triangles—AAS and HL		1. Proving triangles congruent by AAS 2. Hypotenuse-Leg Theorem
Lesson 25: Congruence Criteria for Triangles—AAS and HL
1. Proving triangles congruent by AAS 2. Hypotenuse-Leg Theorem

Lessons 26 & 27: Triangle Congruency Proofs		1. SSS, SAS, ASA, and AAS Theorems 2. Proving triangles congruent by SSS, SAS, ASA, and AAS 3. Proofs involving isosceles triangles
Lessons 26 & 27: Triangle Congruency Proofs
1. SSS, SAS, ASA, and AAS Theorems 2. Proving triangles congruent by SSS, SAS, ASA, and AAS 3. Proofs involving isosceles triangles

Checkpoint opportunity		1. Checkpoint: Rigid motion and congruence
Checkpoint opportunity
1. Checkpoint: Rigid motion and congruence
Topic E - Proving Properties of Geometric Figures
Lesson 28: Properties of Parallelograms		1. Properties of parallelograms 2. Proving a quadrilateral is a parallelogram 3. Properties of rhombuses 4. Properties of squares and rectangles
Lesson 28: Properties of Parallelograms
1. Properties of parallelograms 2. Proving a quadrilateral is a parallelogram 3. Properties of rhombuses 4. Properties of squares and rectangles

Lesson 29: Special Lines in Triangles		1. Midsegments of triangles 2. Proofs involving the Triangle Midsegment Theorem
Lesson 29: Special Lines in Triangles
1. Midsegments of triangles 2. Proofs involving the Triangle Midsegment Theorem

Lesson 30: Special Lines in Triangles		1. Construct the centroid of a triangle
Lesson 30: Special Lines in Triangles
1. Construct the centroid of a triangle

Checkpoint opportunity		1. Checkpoint: Parallelogram theorems
Checkpoint opportunity
1. Checkpoint: Parallelogram theorems
Topic F - Advanced Constructions
Lesson 31: Construct a Square and a Nine-Point Circle		1. Construct a square
Lesson 31: Construct a Square and a Nine-Point Circle
1. Construct a square

Lesson 32: Construct a Nine-Point Circle		1. Construct a square inscribed in a circle
Lesson 32: Construct a Nine-Point Circle
1. Construct a square inscribed in a circle
Topic G - Axiomatic Systems
Lessons 33 & 34: Review of the Assumptions		1. Transversals: name corresponding angles 2. Transversals of parallel lines: prove angle relationships 3. Transversals: prove lines are parallel 4. Proofs involving corresponding parts of congruent triangles 5. Review: properties of quadrilaterals
Lessons 33 & 34: Review of the Assumptions
1. Transversals: name corresponding angles 2. Transversals of parallel lines: prove angle relationships 3. Transversals: prove lines are parallel 4. Proofs involving corresponding parts of congruent triangles 5. Review: properties of quadrilaterals

2	Module 2 Similarity, Proof, and Trigonometry
Topic A - Scale Drawings
Lesson 1: Scale Drawings Lesson 2: Making Scale Drawings Using the Ratio Method Lesson 3: Making Scale Drawings Using the Parallel Method		1. Scale drawings: word problems 2. Scaled polygons
Lesson 1: Scale Drawings Lesson 2: Making Scale Drawings Using the Ratio Method Lesson 3: Making Scale Drawings Using the Parallel Method
1. Scale drawings: word problems 2. Scaled polygons

Lesson 4:Comparing the Ratio Method with the Parallel Method Lesson 5: Scale Factors		1. Triangle Proportionality Theorem 2. Proofs involving the Triangle Proportionality Theorem
Lesson 4:Comparing the Ratio Method with the Parallel Method Lesson 5: Scale Factors
1. Triangle Proportionality Theorem 2. Proofs involving the Triangle Proportionality Theorem
Topic B - Dilations
Lesson 6: Dilations as Transformations of the Plane		1. Dilations: graph the image 2. Dilations: find the scale factor Also consider: • Dilations: find the coordinates
Lesson 6: Dilations as Transformations of the Plane
1. Dilations: graph the image 2. Dilations: find the scale factor Also consider: • Dilations: find the coordinates

Lesson 7: How Do Dilations Map Segments? Lesson 8: How Do Dilations Matp Lines, Rays, and Circles? Lesson 9: How Do Dilations Map Angles?		1. Dilations and parallel lines 2. Dilations: find length, perimeter, and area
Lesson 7: How Do Dilations Map Segments? Lesson 8: How Do Dilations Matp Lines, Rays, and Circles? Lesson 9: How Do Dilations Map Angles?
1. Dilations and parallel lines 2. Dilations: find length, perimeter, and area

Lesson 10: Dividing the King's Foot into 12 Equal Pieces
Lesson 10: Dividing the King's Foot into 12 Equal Pieces


Lesson 11: Dilations from Different Centers		1. Dilations: find the scale factor and center of dilation
Lesson 11: Dilations from Different Centers
1. Dilations: find the scale factor and center of dilation

Checkpoint opportunity		1. Checkpoint: Transformations in the plane 2. Checkpoint: Dilations
Checkpoint opportunity
1. Checkpoint: Transformations in the plane 2. Checkpoint: Dilations
Topic C - Similarity and Dilations
Lesson 12: What Are Similarity Transformations, and Why Do We Need Them?
Lesson 12: What Are Similarity Transformations, and Why Do We Need Them?


Lesson 13: Properties of Similarity Transformations		1. Similar triangles and similarity transformations
Lesson 13: Properties of Similarity Transformations
1. Similar triangles and similarity transformations

Lesson 14: Similarity		1. Identify similar figures 2. Similarity of circles Also consider: • Ratios in similar figures • Similarity statements
Lesson 14: Similarity
1. Identify similar figures 2. Similarity of circles Also consider: • Ratios in similar figures • Similarity statements

Lesson 15: The Angle-Angle (AA) Criterion for Two Triangles to Be Similar		1. Angle-angle criterion for similar triangles 2. Side lengths and angle measures in similar figures
Lesson 15: The Angle-Angle (AA) Criterion for Two Triangles to Be Similar
1. Angle-angle criterion for similar triangles 2. Side lengths and angle measures in similar figures

Lesson 16: Between-Figure and Within-Figure Ratios		1. Similar triangles and indirect measurement
Lesson 16: Between-Figure and Within-Figure Ratios
1. Similar triangles and indirect measurement

Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar		1. Similarity rules for triangles 2. Prove similarity statements Also consider: • Prove proportions or angle congruences using similarity
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
1. Similarity rules for triangles 2. Prove similarity statements Also consider: • Prove proportions or angle congruences using similarity

Lesson 18: Similarity and the Angle Bisector Theorem
Lesson 18: Similarity and the Angle Bisector Theorem


Lesson 19: Families of Parallel Lines and the Circumference of the Earth
Lesson 19: Families of Parallel Lines and the Circumference of the Earth


Lesson 20: How Far Away Is the Moon?
Lesson 20: How Far Away Is the Moon?


Checkpoint opportunity		1. Checkpoint: Prove circles are similar 2. Checkpoint: Similarity transformations
Checkpoint opportunity
1. Checkpoint: Prove circles are similar 2. Checkpoint: Similarity transformations
Topic D - Applying Similarity to Right Triangles
Lesson 21: Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles		1. Similarity and altitudes in right triangles Also consider: • Proofs involving similarity in right triangles
Lesson 21: Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles
1. Similarity and altitudes in right triangles Also consider: • Proofs involving similarity in right triangles

Lesson 22: Multiplying and Dividing Expressions with Radicals		1. Multiplying and dividing expressions with radicals
Lesson 22: Multiplying and Dividing Expressions with Radicals
1. Multiplying and dividing expressions with radicals

Lesson 23: Adding and Subtracting Expressions with Radicals		1. Adding and subtracting expressions with radicals
Lesson 23: Adding and Subtracting Expressions with Radicals
1. Adding and subtracting expressions with radicals

Lesson 24: Prove the Pythagorean Theorem Using Similarity		1. Prove the Pythagorean theorem 2. Special right triangles Also consider: • Pythagorean theorem
Lesson 24: Prove the Pythagorean Theorem Using Similarity
1. Prove the Pythagorean theorem 2. Special right triangles Also consider: • Pythagorean theorem

Checkpoint opportunity		1. Checkpoint: Triangle similarity and congruence
Checkpoint opportunity
1. Checkpoint: Triangle similarity and congruence
Topic E - Trigonometry
Lesson 25: Incredibly Useful Ratios
Lesson 25: Incredibly Useful Ratios


Lesson 26: The Definition of Sine, Cosine, and Tangent		1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan Also consider: • Trigonometric ratios: csc, sec, and cot • Trigonometric ratios in similar right triangles
Lesson 26: The Definition of Sine, Cosine, and Tangent
1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan Also consider: • Trigonometric ratios: csc, sec, and cot • Trigonometric ratios in similar right triangles

Lesson 27: Sine and Cosine of Complementary Angles and Special Angles		1. Sine and cosine of complementary angles 2. Sine and cosine of special angles 3. Use sine and cosine to solve a special right triangle
Lesson 27: Sine and Cosine of Complementary Angles and Special Angles
1. Sine and cosine of complementary angles 2. Sine and cosine of special angles 3. Use sine and cosine to solve a special right triangle

Lesson 28: Solving Problems Using Sine and Cosine Lesson 29: Applying Tangents		1. Find trigonometric functions using a calculator 2. Trigonometric ratios: find a side length
Lesson 28: Solving Problems Using Sine and Cosine Lesson 29: Applying Tangents
1. Find trigonometric functions using a calculator 2. Trigonometric ratios: find a side length

Lesson 30: Trigonometry and the Pythagorean Theorem		1. Solve a right triangle
Lesson 30: Trigonometry and the Pythagorean Theorem
1. Solve a right triangle

Lesson 31: Using Trigonometry to Determine Area		1. Area of a triangle: sine formula
Lesson 31: Using Trigonometry to Determine Area
1. Area of a triangle: sine formula

Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle Lesson 33: Applying the Laws of Sines and Cosines Lesson 34: Unknown Angles		1. Trigonometric ratios: find an angle measure 2. Law of Sines 3. Law of Cosines Also consider: • Inverses of trigonometric functions • Solve a triangle • Area of a triangle: Law of Sines
Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle Lesson 33: Applying the Laws of Sines and Cosines Lesson 34: Unknown Angles
1. Trigonometric ratios: find an angle measure 2. Law of Sines 3. Law of Cosines Also consider: • Inverses of trigonometric functions • Solve a triangle • Area of a triangle: Law of Sines

Checkpoint opportunity		1. Checkpoint: Right triangle trigonometry 2. Checkpoint: Laws of Sines and Cosines
Checkpoint opportunity
1. Checkpoint: Right triangle trigonometry 2. Checkpoint: Laws of Sines and Cosines

3	Module 3 Extending to Three Dimensions
Topic A - Area
Lesson 1: What Is Area? Lesson 2: Properties of Area		1. Area of compound figures 2. Area between two shapes Also consider: • Area: mixed review • Area of circles
Lesson 1: What Is Area? Lesson 2: Properties of Area
1. Area of compound figures 2. Area between two shapes Also consider: • Area: mixed review • Area of circles

Lesson 3: The Scaling Principle for Area		1. Areas of similar figures
Lesson 3: The Scaling Principle for Area
1. Areas of similar figures

Lesson 4: Proving the Area of a Disk		1. Area of equilateral triangles and regular hexagons
Lesson 4: Proving the Area of a Disk
1. Area of equilateral triangles and regular hexagons
Topic B - Volume
Lesson 5: Three-Dimensional Space		1. Identify parallel, intersecting, and skew lines and planes 2. Properties of planes, lines, and points
Lesson 5: Three-Dimensional Space
1. Identify parallel, intersecting, and skew lines and planes 2. Properties of planes, lines, and points

Lesson 6: General Prisms and Cylinders and Their Cross-Sections Lesson 7: General Pyramids and Cones and Their Cross-Sections		1. Cross sections of three-dimensional figures 2. Solids of revolution Also consider: • Volume of prisms • Surface area of prisms and cylinders • Lateral area of prisms and cylinders
Lesson 6: General Prisms and Cylinders and Their Cross-Sections Lesson 7: General Pyramids and Cones and Their Cross-Sections
1. Cross sections of three-dimensional figures 2. Solids of revolution Also consider: • Volume of prisms • Surface area of prisms and cylinders • Lateral area of prisms and cylinders

Lesson 8: Definition and Properties of Volume		1. Volume of cylinders 2. Volume of complex prisms Also consider: • Calculate density, mass, and volume
Lesson 8: Definition and Properties of Volume
1. Volume of cylinders 2. Volume of complex prisms Also consider: • Calculate density, mass, and volume

Lesson 9: Scaling Principle for Volumes		1. Similar solids: find the missing length 2. Volume of similar prisms and cylinders
Lesson 9: Scaling Principle for Volumes
1. Similar solids: find the missing length 2. Volume of similar prisms and cylinders

Lesson 10: The Volume of Prisms and Cylinders and Cavalieri's Principle
Lesson 10: The Volume of Prisms and Cylinders and Cavalieri's Principle


Lesson 11: The Volume Formula of a Pyramid and Cone Lesson 12: The Volume Formula of a Sphere		1. Volume of pyramids and cones 2. Volume of spheres Also consider: • Lateral area of pyramids and cones
Lesson 11: The Volume Formula of a Pyramid and Cone Lesson 12: The Volume Formula of a Sphere
1. Volume of pyramids and cones 2. Volume of spheres Also consider: • Lateral area of pyramids and cones

Lesson 13: How Do 3D Printers Work?
Lesson 13: How Do 3D Printers Work?


Checkpoint opportunity		1. Checkpoint: Volume 2. Checkpoint: Cross sections and solids of revolution 3. Checkpoint: Geometric modeling and design 4. Checkpoint: Density
Checkpoint opportunity
1. Checkpoint: Volume 2. Checkpoint: Cross sections and solids of revolution 3. Checkpoint: Geometric modeling and design 4. Checkpoint: Density

4	Module 4 Connecting Algebra and Geometry Through Coordinates
Topic A - Rectangular and Triangular Regions Defined by Inequalities
Lesson 1: Searching a Region in the Plane		1. Distance formula 2. Rate of travel: word problems Also consider: • Coordinate plane review • Slopes of lines
Lesson 1: Searching a Region in the Plane
1. Distance formula 2. Rate of travel: word problems Also consider: • Coordinate plane review • Slopes of lines

Lesson 2: Finding Systems of Inequalities That Describe Triangular and Rectangular Regions		1. Graph a two-variable linear inequality 2. Write a linear inequality from a graph
Lesson 2: Finding Systems of Inequalities That Describe Triangular and Rectangular Regions
1. Graph a two-variable linear inequality 2. Write a linear inequality from a graph

Lesson 3: Lines That Pass Through Regions		1. Describe intersections in a plane
Lesson 3: Lines That Pass Through Regions
1. Describe intersections in a plane

Lesson 4: Designing a Search Robot to Find a Beacon		1. Equations of lines 2. Point-slope form: write an equation
Lesson 4: Designing a Search Robot to Find a Beacon
1. Equations of lines 2. Point-slope form: write an equation
Topic B - Perpendicular and Parallel Lines in the Cartesian Plane
Lesson 5: Criterion for Perpendicularity Lesson 6: Segments That Meet at Right Angles		1. Converse of the Pythagorean theorem 2. Classify triangles on the coordinate plane: justify your answer
Lesson 5: Criterion for Perpendicularity Lesson 6: Segments That Meet at Right Angles
1. Converse of the Pythagorean theorem 2. Classify triangles on the coordinate plane: justify your answer

Lesson 7: Equations for Lines Using Normal Segments
Lesson 7: Equations for Lines Using Normal Segments


Lesson 8: Parallel and Perpendicular Lines		1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines
Lesson 8: Parallel and Perpendicular Lines
1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines

Checkpoint opportunity		1. Checkpoint: Parallel and perpendicular lines
Checkpoint opportunity
1. Checkpoint: Parallel and perpendicular lines
Topic C - Perimeters and Areas of Polygonal Regions in the Cartesian Plane
Lesson 9: Perimeter and Area of Triangles in the Cartesian Plane		1. Area and perimeter in the coordinate plane I
Lesson 9: Perimeter and Area of Triangles in the Cartesian Plane
1. Area and perimeter in the coordinate plane I

Lesson 10: Perimeter and Area of Polygonal Regions in the Cartesian Plane		1. Area and perimeter in the coordinate plane II
Lesson 10: Perimeter and Area of Polygonal Regions in the Cartesian Plane
1. Area and perimeter in the coordinate plane II

Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities
Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities


Checkpoint opportunity		1. Checkpoint: Area and perimeter in the coordinate plane
Checkpoint opportunity
1. Checkpoint: Area and perimeter in the coordinate plane
Topic D - Partitioning and Extending Segments and Parameterization of Lines
Lesson 12: Dividing Segments Proportionately		1. Midpoint formula: find the midpoint 2. Partition a line segment in a given ratio Also consider: • Midpoint formula: find the endpoint
Lesson 12: Dividing Segments Proportionately
1. Midpoint formula: find the midpoint 2. Partition a line segment in a given ratio Also consider: • Midpoint formula: find the endpoint

Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means		1. Find the centroid of a triangle 2. Classify quadrilaterals on the coordinate plane: justify your answer
Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means
1. Find the centroid of a triangle 2. Classify quadrilaterals on the coordinate plane: justify your answer

Lesson 14: Motion Along a Line—Search Robots Again
Lesson 14: Motion Along a Line—Search Robots Again


Lesson 15: The Distance from a Point to a Line		1. Find the distance between a point and a line
Lesson 15: The Distance from a Point to a Line
1. Find the distance between a point and a line

Checkpoint opportunity		1. Checkpoint: Triangle theorems 2. Checkpoint: Partition a line segment
Checkpoint opportunity
1. Checkpoint: Triangle theorems 2. Checkpoint: Partition a line segment

5	Module 5 Circles With and Without Coordinates
Topic A - Central and Inscribed Angles
Lesson 1: Thales' Theorem		1. Parts of a circle 2. Angles in inscribed right triangles
Lesson 1: Thales' Theorem
1. Parts of a circle 2. Angles in inscribed right triangles

Lesson 2: Circles, Chords, Diameters, and Their Relationships		1. Central angles and chords
Lesson 2: Circles, Chords, Diameters, and Their Relationships
1. Central angles and chords

Lesson 3: Rectangles Inscribed in Circles
Lesson 3: Rectangles Inscribed in Circles


Lesson 4: Experiments with Inscribed Angles Lesson 5: Inscribed Angle Theorem and Its Applications Lesson 6: Unknown Angle Problems with Inscribed Angles in Circles		1. Inscribed angle theorem I
Lesson 4: Experiments with Inscribed Angles Lesson 5: Inscribed Angle Theorem and Its Applications Lesson 6: Unknown Angle Problems with Inscribed Angles in Circles
1. Inscribed angle theorem I
Topic B - Arcs and Sectors
Lesson 7: The Angle Measure of an Arc		1. Central angles and arc measures 2. Inscribed angle theorem II
Lesson 7: The Angle Measure of an Arc
1. Central angles and arc measures 2. Inscribed angle theorem II

Lesson 8: Arcs and Chords		1. Arcs and chords
Lesson 8: Arcs and Chords
1. Arcs and chords

Lesson 9: Arc Length and Areas of Sectors		1. Arc length 2. Area of sectors 3. Radians and arc length Also consider: • Understand arc length and sector area of a circle • Convert between radians and degrees
Lesson 9: Arc Length and Areas of Sectors
1. Arc length 2. Area of sectors 3. Radians and arc length Also consider: • Understand arc length and sector area of a circle • Convert between radians and degrees

Lesson 10: Unknown Length and Area Problems		1. Circle measurements: mixed review
Lesson 10: Unknown Length and Area Problems
1. Circle measurements: mixed review

Checkpoint opportunity		1. Checkpoint: Arc length and area of sectors
Checkpoint opportunity
1. Checkpoint: Arc length and area of sectors
Topic C - Secants and Tangents
Lesson 11: Properties of Tangents		1. Tangent lines 2. Construct a tangent line to a circle
Lesson 11: Properties of Tangents
1. Tangent lines 2. Construct a tangent line to a circle

Lesson 12: Tangent Segments		1. Perimeter of polygons with an inscribed circle
Lesson 12: Tangent Segments
1. Perimeter of polygons with an inscribed circle

Lesson 13: The Inscribed Angle Alternate—A Tangent Angle		1. Angles formed by tangents and chords or secants
Lesson 13: The Inscribed Angle Alternate—A Tangent Angle
1. Angles formed by tangents and chords or secants

Lesson 14: Secant Lines; Secant Lines That Meet Inside a Circle Lesson 15: Secant Angle Theorem, Exterior Case		1. Angles formed by chords, secants, and tangents
Lesson 14: Secant Lines; Secant Lines That Meet Inside a Circle Lesson 15: Secant Angle Theorem, Exterior Case
1. Angles formed by chords, secants, and tangents

Lesson 16: Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams		1. Segments formed by chords, secants, and tangents
Lesson 16: Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams
1. Segments formed by chords, secants, and tangents

Checkpoint opportunity		1. Checkpoint: Angles and lines in circles 2. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Angles and lines in circles 2. Checkpoint: Geometric constructions
Topic D - Equations for Circles and Their Tangents
Lesson 17: Writing the Equation for a Circle		1. Derive equations of circles using the Pythagorean theorem 2. Write equations of circles in standard form from graphs 3. Write equations of circles in standard form using properties Also consider: • Find the center of a circle • Find the radius or diameter of a circle • Graph circles from equations in standard form
Lesson 17: Writing the Equation for a Circle
1. Derive equations of circles using the Pythagorean theorem 2. Write equations of circles in standard form from graphs 3. Write equations of circles in standard form using properties Also consider: • Find the center of a circle • Find the radius or diameter of a circle • Graph circles from equations in standard form

Lesson 18: Recognizing Equations of Circles		1. Convert equations of circles from general to standard form 2. Find properties of circles from equations in general form Also consider: • Graph circles from equations in general form
Lesson 18: Recognizing Equations of Circles
1. Convert equations of circles from general to standard form 2. Find properties of circles from equations in general form Also consider: • Graph circles from equations in general form

Lesson 19: Equations for Tangent Lines to Circles		1. Determine if a point lies on a circle
Lesson 19: Equations for Tangent Lines to Circles
1. Determine if a point lies on a circle

Checkpoint opportunity		1. Checkpoint: Equations of circles 2. Checkpoint: Coordinate proofs
Checkpoint opportunity
1. Checkpoint: Equations of circles 2. Checkpoint: Coordinate proofs
Topic E - Cyclic Quadrilaterals and Ptolemy's Theorem
Lesson 20: Cyclic Quadrilaterals		1. Angles in inscribed quadrilaterals I 2. Angles in inscribed quadrilaterals II
Lesson 20: Cyclic Quadrilaterals
1. Angles in inscribed quadrilaterals I 2. Angles in inscribed quadrilaterals II

Lesson 21: Ptolemy's Theorem
Lesson 21: Ptolemy's Theorem


Checkpoint opportunity		1. Checkpoint: Inscribed and circumscribed circles
Checkpoint opportunity
1. Checkpoint: Inscribed and circumscribed circles

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