# Geometry and spatial reasoning

Here is a list of all of the skills that cover geometry and spatial reasoning! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Pre-K skills

- F.1 Inside and outside
- F.2 Left and right
- F.3 Left, middle, and right
- F.4 Top and bottom
- F.5 Top, middle, and bottom
- F.6 Above and below
- F.7 Beside and next to
- K.1 Name the shape
- K.2 Circles
- K.3 Squares
- K.4 Triangles
- K.5 Rectangles
- K.6 Circles, squares, and triangles
- L.1 Flat and solid shapes
- L.2 Name the solid shape
- L.3 Spheres
- L.4 Cubes
- L.5 Cones
- L.6 Cylinders
- L.7 Select solid shapes

## Kindergarten skills

- M.1 Inside and outside
- M.2 Left, middle, and right
- M.3 Top, middle, and bottom
- M.4 Location in a grid
- M.5 Above and below
- M.6 Above and below - find solid figures
- M.7 Beside and next to
- M.8 Beside and next to - find solid figures
- P.8 Count shapes in a Venn diagram
- P.9 Sort shapes into a Venn diagram
- V.1 Name the two-dimensional shape
- V.2 Circles
- V.3 Squares and rectangles
- V.4 Hexagons
- V.5 Select two-dimensional shapes
- V.6 Count sides and corners
- V.7 Compare sides and corners
- V.8 Introduction to symmetry
- V.9 Identify pictures with symmetry
- W.1 Two-dimensional and three-dimensional shapes
- W.2 Name the three-dimensional shape
- W.3 Spheres
- W.4 Cubes
- W.5 Cones
- W.6 Cylinders
- W.7 Select three-dimensional shapes
- W.8 Identify shapes traced from solids
- W.9 Shapes of everyday objects I
- W.10 Shapes of everyday objects II

## First-grade skills

- N.1 Left, middle, and right
- N.2 Top, middle, and bottom
- N.3 Location in a grid
- N.4 Above and below
- N.5 Beside and next to
- T.1 Count shapes in a Venn diagram
- T.2 Sort shapes into a Venn diagram
- V.1 Name the two-dimensional shape
- V.2 Select two-dimensional shapes
- V.3 Count sides and vertices
- V.4 Compare sides and vertices
- V.5 Open and closed shapes
- V.6 Flip, turn, and slide
- V.7 Symmetry
- W.1 Two-dimensional and three-dimensional shapes
- W.2 Name the three-dimensional shape
- W.3 Cubes and rectangular prisms
- W.4 Select three-dimensional shapes
- W.5 Count vertices, edges, and faces
- W.6 Compare vertices, edges, and faces
- W.7 Identify shapes traced from solids
- W.8 Identify faces of three-dimensional shapes
- W.9 Shapes of everyday objects I
- W.10 Shapes of everyday objects II

## Second-grade skills

- R.14 Count shapes in a Venn diagram
- R.15 Sort shapes into a Venn diagram
- T.1 Name the two-dimensional shape
- T.2 Select two-dimensional shapes
- T.3 Count sides and vertices
- T.4 Compare sides and vertices
- T.5 Flip, turn, and slide
- T.6 Identify congruent shapes
- T.7 Symmetry
- U.1 Name the three-dimensional shape
- U.2 Select three-dimensional shapes
- U.3 Count vertices, edges, and faces
- U.4 Compare vertices, edges, and faces
- U.5 Identify faces of three-dimensional shapes
- U.6 Identify shapes traced from solids
- U.7 Shapes of everyday objects I
- U.8 Shapes of everyday objects II
- V.1 Perimeter
- V.2 Perimeter - word problems
- V.3 Area
- V.4 Select figures with a given area
- V.5 Create figures with a given area

## Third-grade skills

- U.15 Count shapes in a Venn diagram
- U.16 Sort shapes into a Venn diagram
- CC.1 Identify two-dimensional shapes
- CC.2 Count and compare sides and vertices
- CC.3 Open and closed shapes
- CC.4 Is it a polygon?
- CC.5 Lines, line segments, and rays
- CC.6 Angles greater than, less than, or equal to a right angle
- CC.7 Parallel, perpendicular, and intersecting lines
- CC.8 Reflection, rotation, and translation
- CC.9 Identify congruent shapes
- CC.10 Symmetry
- DD.1 Acute, obtuse, and right triangles
- DD.2 Scalene, isosceles, and equilateral triangles
- DD.3 Parallel sides in quadrilaterals
- DD.4 Identify parallelograms
- DD.5 Identify trapezoids
- DD.6 Identify rectangles
- DD.7 Identify rhombuses
- DD.8 Classify quadrilaterals
- EE.1 Identify three-dimensional shapes
- EE.2 Count vertices, edges, and faces
- EE.3 Identify faces of three-dimensional shapes
- EE.4 Shapes of everyday objects I
- EE.5 Shapes of everyday objects II
- FF.1 Perimeter of rectangles
- FF.2 Perimeter of rectilinear shapes
- FF.3 Perimeter of polygons
- FF.4 Perimeter: find the missing side length
- FF.5 Perimeter: word problems
- FF.6 Find the area of figures made of unit squares
- FF.7 Select figures with a given area
- FF.8 Select two figures with the same area
- FF.9 Create figures with a given area
- FF.10 Find the area of rectangles and squares
- FF.11 Find the missing side length of a rectangle
- FF.12 Find the area of rectangles with missing unit squares
- FF.13 Find the area of rectangles: word problems
- FF.14 Find the area of complex figures
- FF.15 Find the area between two rectangles
- FF.16 Compare area and perimeter of two figures
- FF.17 Use area and perimeter to determine cost
- FF.18 Relationship between area and perimeter I
- FF.19 Relationship between area and perimeter II
- FF.20 Volume

## Fourth-grade skills

- W.1 Open and closed shapes
- W.2 Is it a polygon?
- W.3 Number of sides in polygons
- W.4 Lines, line segments, and rays
- W.5 Parallel, perpendicular, and intersecting lines
- W.6 Identify congruent figures
- W.7 Parts of a circle
- X.1 Acute, obtuse, and right triangles
- X.2 Scalene, isosceles, and equilateral triangles
- X.3 Classify triangles
- X.4 Parallel sides in quadrilaterals
- X.5 Identify parallelograms
- X.6 Identify trapezoids
- X.7 Identify rectangles
- X.8 Identify rhombuses
- X.9 Classify quadrilaterals
- Y.1 Identify lines of symmetry
- Y.2 Draw lines of symmetry
- Y.3 Count lines of symmetry
- Y.4 Rotational symmetry
- Z.1 Acute, right, obtuse, and straight angles
- Z.2 Angles of 90, 180, 270, and 360 degrees
- Z.3 Measure angles with a protractor
- Z.4 Estimate angle measurements
- Z.5 Adjacent angles
- AA.1 Identify three-dimensional figures
- AA.2 Count vertices, edges, and faces
- AA.3 Identify faces of three-dimensional figures
- AA.4 Properties of three-dimensional figures
- AA.5 Nets of three-dimensional figures
- BB.1 Perimeter
- BB.2 Perimeter: find the missing side lengths
- BB.3 Select figures with a given area
- BB.4 Select two figures with the same area
- BB.5 Create figures with a given area
- BB.6 Find the area or missing side length of a rectangle
- BB.7 Area of complex figures (with all right angles)
- BB.8 Area between two rectangles
- BB.9 Compare area and perimeter of two figures
- BB.10 Relationship between area and perimeter
- BB.11 Area and perimeter: word problems
- BB.12 Rectangles: relationship between perimeter and area word problems
- BB.13 Volume
- BB.14 Use area and perimeter to determine cost
- BB.15 Calculate radius, diameter, and circumference

## Fifth-grade skills

- AA.1 Is it a polygon?
- AA.2 Number of sides in polygons
- AA.3 Regular and irregular polygons
- AA.4 Lines, line segments, and rays
- AA.5 Parallel, perpendicular, and intersecting lines
- AA.6 Types of angles
- AA.7 Measure angles with a protractor
- AA.8 Find the unknown angle in triangles and quadrilaterals
- AA.9 Parts of a circle
- BB.1 Acute, obtuse, and right triangles
- BB.2 Scalene, isosceles, and equilateral triangles
- BB.3 Classify triangles
- BB.4 Parallel sides in quadrilaterals
- BB.5 Identify parallelograms
- BB.6 Identify trapezoids
- BB.7 Identify rectangles
- BB.8 Identify rhombuses
- BB.9 Classify quadrilaterals
- CC.1 Lines of symmetry
- CC.2 Rotational symmetry
- CC.3 Reflection, rotation, and translation
- CC.4 Identify congruent and similar figures
- DD.1 Identify three-dimensional figures
- DD.2 Count vertices, edges, and faces
- DD.3 Nets of three-dimensional figures
- DD.4 Three-dimensional figures viewed from different perspectives
- EE.1 Perimeter with whole number side lengths
- EE.2 Perimeter with decimal side lengths
- EE.3 Perimeter with fractional side lengths
- EE.4 Area of squares and rectangles
- EE.5 Area of triangles
- EE.6 Area of parallelograms and trapezoids
- EE.7 Area of compound figures
- EE.8 Area between two rectangles
- EE.9 Area and perimeter of figures on grids
- EE.10 Area and perimeter: word problems
- EE.11 Volume of rectangular prisms made of unit cubes
- EE.12 Volume of irregular figures made of unit cubes
- EE.13 Volume of cubes and rectangular prisms
- EE.14 Volume of cubes and rectangular prisms with decimal side lengths
- EE.15 Surface area
- EE.16 Radius, diameter, circumference, and area of a circle

## Sixth-grade skills

- X.5 Distance between two points
- CC.1 Identify and classify polygons
- CC.2 Measure and classify angles
- CC.3 Estimate angle measurements
- CC.4 Classify triangles
- CC.5 Identify trapezoids
- CC.6 Classify quadrilaterals
- CC.7 Graph triangles and quadrilaterals
- CC.8 Find missing angles in triangles
- CC.9 Find missing angles in quadrilaterals
- CC.10 Sums of angles in polygons
- CC.11 Lines, line segments, and rays
- CC.12 Name angles
- CC.13 Complementary and supplementary angles
- CC.14 Transversal of parallel lines
- CC.15 Find lengths and measures of bisected line segments and angles
- CC.16 Parts of a circle
- CC.17 Central angles of circles
- DD.1 Symmetry
- DD.2 Reflection, rotation, and translation
- DD.3 Translations: graph the image
- DD.4 Reflections: graph the image
- DD.5 Rotations: graph the image
- DD.6 Similar and congruent figures
- DD.7 Find side lengths of similar figures
- EE.1 Identify polyhedra
- EE.2 Which figure is being described?
- EE.3 Nets of three-dimensional figures
- EE.4 Front, side, and top view
- FF.1 Perimeter
- FF.2 Area of rectangles and squares
- FF.3 Area of triangles
- FF.4 Area of parallelograms and trapezoids
- FF.5 Area of quadrilaterals
- FF.6 Area of compound figures
- FF.7 Area between two rectangles
- FF.8 Area between two triangles
- FF.9 Rectangles: relationship between perimeter and area
- FF.10 Compare area and perimeter of two figures
- FF.11 Circles: calculate area, circumference, radius, and diameter
- FF.12 Circles: word problems
- FF.13 Area between two circles
- FF.14 Volume of cubes and rectangular prisms
- FF.15 Surface area of cubes and rectangular prisms
- FF.16 Volume and surface area of triangular prisms
- FF.17 Volume and surface area of cylinders
- FF.18 Relate volume and surface area
- FF.19 Semicircles: calculate area, perimeter, radius, and diameter
- FF.20 Quarter circles: calculate area, perimeter, and radius
- FF.21 Area of compound figures with triangles, semicircles, and quarter circles

## Seventh-grade skills

- P.4 Distance between two points
- W.1 Identify and classify polygons
- W.2 Name, measure, and classify angles
- W.3 Classify triangles
- W.4 Identify trapezoids
- W.5 Classify quadrilaterals
- W.6 Graph triangles and quadrilaterals
- W.7 Find missing angles in triangles
- W.8 Find missing angles in quadrilaterals
- W.9 Interior angles of polygons
- W.10 Lines, line segments, and rays
- W.11 Parallel, perpendicular, and intersecting lines
- W.12 Identify complementary, supplementary, vertical, adjacent, and congruent angles
- W.13 Find measures of complementary, supplementary, vertical, and adjacent angles
- W.14 Transversal of parallel lines
- W.15 Find lengths and measures of bisected line segments and angles
- W.16 Parts of a circle
- X.1 Symmetry
- X.2 Identify reflections, rotations, and translations
- X.3 Translations: graph the image
- X.4 Translations: find the coordinates
- X.5 Reflections: graph the image
- X.6 Reflections: find the coordinates
- X.7 Rotations: graph the image
- X.8 Rotations: find the coordinates
- X.9 Similar and congruent figures
- X.10 Congruence statements and corresponding parts
- X.11 Side lengths and angle measures of congruent figures
- X.12 Side lengths and angle measures of similar figures
- X.13 Similar figures and indirect measurement
- Y.1 Pythagorean theorem: find the length of the hypotenuse
- Y.2 Pythagorean theorem: find the missing leg length
- Y.3 Pythagorean theorem: word problems
- Y.4 Converse of the Pythagorean theorem: is it a right triangle?
- Z.1 Bases of three-dimensional figures
- Z.2 Nets of three-dimensional figures
- Z.3 Front, side, and top view
- Z.4 Cross-sections of three-dimensional figures
- AA.1 Perimeter
- AA.2 Area of rectangles and parallelograms
- AA.3 Area of triangles and trapezoids
- AA.4 Area and perimeter: word problems
- AA.5 Circles: calculate area, circumference, radius, and diameter
- AA.6 Circles: word problems
- AA.7 Volume
- AA.8 Surface area
- AA.9 Perimeter, area, and volume: changes in scale
- AA.10 Semicircles: calculate area, perimeter, radius, and diameter
- AA.11 Quarter circles: calculate area, perimeter, and radius
- AA.12 Area of compound figures with triangles, semicircles, and quarter circles
- AA.13 Area between two shapes

## Eighth-grade skills

- N.4 Find the distance between two points
- O.1 Identify and classify polygons
- O.2 Classify triangles
- O.3 Identify trapezoids
- O.4 Classify quadrilaterals
- O.5 Graph triangles and quadrilaterals
- O.6 Find missing angles in triangles
- O.7 Find missing angles in quadrilaterals
- O.8 Exterior Angle Theorem
- O.9 Interior angles of polygons
- O.10 Identify complementary, supplementary, vertical, adjacent, and congruent angles
- O.11 Find measures of complementary, supplementary, vertical, and adjacent angles
- O.12 Transversal of parallel lines
- O.13 Find lengths and measures of bisected line segments and angles
- O.14 Parts of a circle
- P.1 Symmetry
- P.2 Identify reflections, rotations, and translations
- P.3 Translations: graph the image
- P.4 Translations: find the coordinates
- P.5 Reflections: graph the image
- P.6 Reflections: find the coordinates
- P.7 Rotations: graph the image
- P.8 Rotations: find the coordinates
- P.9 Congruence statements and corresponding parts
- P.10 Side lengths and angle measures of congruent figures
- P.11 Congruent triangles: SSS, SAS, and ASA
- Q.1 Similar and congruent figures
- Q.2 Dilations: graph the image
- Q.3 Dilations: find the coordinates
- Q.4 Dilations: scale factor and classification
- Q.5 Side lengths and angle measures of similar figures
- R.1 Pythagorean theorem: find the length of the hypotenuse
- R.2 Pythagorean theorem: find the missing leg length
- R.3 Pythagorean theorem: find the perimeter
- R.4 Pythagorean theorem: word problems
- R.5 Converse of the Pythagorean theorem: is it a right triangle?
- S.1 Parts of three-dimensional figures
- S.2 Nets of three-dimensional figures
- S.3 Front, side, and top view
- S.4 Base plans
- S.5 Similar solids
- T.1 Perimeter
- T.2 Area
- T.3 Area and perimeter: word problems
- T.4 Area between two shapes
- T.5 Circles, semicircles, and quarter circles
- T.6 Circles: word problems
- T.7 Volume of cubes, prisms, and pyramids
- T.8 Surface area of cubes, prisms, and pyramids
- T.9 Volume of cylinders
- T.10 Volume of cones
- T.11 Surface area of cylinders
- T.12 Surface area of cones
- T.13 Volume of spheres
- T.14 Surface area of spheres
- T.15 Volume and surface area of similar solids
- T.16 Perimeter, area, and volume: changes in scale
- BB.5 Add polynomials to find perimeter
- BB.13 Multiply polynomials to find area

## Algebra 1 skills

- E.6 Minimum and maximum area and volume
- E.8 Percent error: area and volume
- F.1 Perimeter
- F.2 Area
- F.3 Area and perimeter: word problems
- F.4 Volume
- F.5 Surface area
- F.6 Similar figures: side lengths and angle measures
- F.7 Similar triangles and indirect measurement
- F.8 Dilations and scale factors
- F.9 Area and perimeter of similar figures
- F.10 Area between two shapes
- F.11 Similar solids
- F.12 Volume and surface area of similar solids
- F.13 Perimeter, area, and volume: changes in scale
- F.14 Pythagorean theorem
- F.15 Pythagorean theorem: word problems
- F.16 Converse of the Pythagorean theorem: is it a right triangle?
- F.17 Special right triangles
- G.2 Midpoint formula - find the midpoint
- G.3 Midpoint formula - find the endpoint
- G.4 Distance between two points
- Z.5 Add polynomials to find perimeter
- HH.1 Trigonometric ratios: sin, cos, and tan
- HH.2 Find trigonometric ratios using a calculator
- HH.3 Inverses of trigonometric functions
- HH.4 Trigonometric ratios: find a side length
- HH.5 Trigonometric ratios: find an angle measure
- HH.6 Solve a right triangle

## Geometry skills

- B.1 Lines, line segments, and rays
- B.2 Lengths of segments on number lines
- B.3 Additive property of length
- B.4 Midpoints
- B.5 Congruent line segments
- B.6 Perpendicular Bisector Theorem
- B.7 Midpoint formula - find the midpoint
- B.8 Midpoint formula - find the endpoint
- B.9 Distance formula
- B.10 Construct the midpoint or perpendicular bisector of a segment
- C.1 Angle vocabulary
- C.2 Angle measures
- C.3 Identify complementary, supplementary, vertical, adjacent, and congruent angles
- C.4 Find measures of complementary, supplementary, vertical, and adjacent angles
- C.5 Angle bisectors
- C.6 Construct an angle bisector
- C.7 Construct a congruent angle
- C.8 Proofs involving angles
- D.1 Identify parallel, perpendicular, and skew lines and planes
- D.2 Construct a perpendicular line
- D.3 Transversals: name angle pairs
- D.4 Transversals of parallel lines: find angle measures
- D.5 Construct parallel lines
- D.6 Proofs involving parallel lines I
- D.7 Proofs involving parallel lines II
- E.7 Find the distance between a point and a line
- E.8 Find the distance between two parallel lines
- F.1 Classify triangles
- F.2 Triangle Angle-Sum Theorem
- F.3 Exterior Angle Theorem
- F.4 Exterior Angle Inequality
- G.1 Polygon vocabulary
- G.2 Interior angles of polygons
- G.3 Exterior angles of polygons
- G.4 Review: interior and exterior angles of polygons
- G.5 Construct an equilateral triangle or regular hexagon
- G.6 Construct a square
- H.1 Parts of three-dimensional figures
- H.2 Three-dimensional figure vocabulary
- H.3 Nets and drawings of three-dimensional figures
- H.4 Cross-sections of three-dimensional figures
- H.5 Solids of revolution
- J.1 Congruence statements and corresponding parts
- J.2 Solve problems involving corresponding parts
- J.3 Identify congruent figures
- K.1 SSS and SAS Theorems
- K.2 Proving triangles congruent by SSS and SAS
- K.3 ASA and AAS Theorems
- K.4 Proving triangles congruent by ASA and AAS
- K.5 SSS, SAS, ASA, and AAS Theorems
- K.6 SSS Theorem in the coordinate plane
- K.7 Proving triangles congruent by SSS, SAS, ASA, and AAS
- K.8 Proofs involving corresponding parts of congruent triangles
- K.9 Congruency in isosceles and equilateral triangles
- K.10 Proofs involving isosceles triangles
- K.11 Hypotenuse-Leg Theorem
- L.1 Classify congruence transformations
- L.2 Translations: graph the image
- L.3 Translations: find the coordinates
- L.4 Translations: write the rule
- L.5 Reflections: graph the image
- L.6 Reflections: find the coordinates
- L.7 Rotate polygons about a point
- L.8 Rotations: graph the image
- L.9 Rotations: find the coordinates
- L.10 Compositions of congruence transformations: graph the image
- L.11 Transformations that carry a polygon onto itself
- L.12 Congruence transformations: mixed review
- L.13 Dilations: graph the image
- L.14 Dilations: find the coordinates
- L.15 Dilations: scale factor and classification
- L.16 Dilations and parallel lines
- M.1 Midsegments of triangles
- M.2 Triangles and bisectors
- M.3 Identify medians, altitudes, angle bisectors, and perpendicular bisectors
- M.4 Angle-side relationships in triangles
- M.5 Triangle Inequality Theorem
- M.6 Construct the circumcenter or incenter of a triangle
- M.7 Construct the centroid or orthocenter of a triangle
- M.8 Proofs involving triangles I
- M.9 Proofs involving triangles II
- N.1 Identify trapezoids
- N.2 Classify quadrilaterals
- N.3 Graph quadrilaterals
- N.4 Properties of parallelograms
- N.5 Proving a quadrilateral is a parallelogram
- N.6 Properties of rhombuses
- N.7 Properties of squares and rectangles
- N.8 Properties of trapezoids
- N.9 Properties of kites
- N.10 Review: properties of quadrilaterals
- N.11 Proofs involving quadrilaterals I
- N.12 Proofs involving quadrilaterals II
- O.1 Line symmetry
- O.2 Rotational symmetry
- O.3 Draw lines of symmetry
- O.4 Count lines of symmetry
- P.1 Similarity ratios
- P.2 Similarity statements
- P.3 Identify similar figures
- P.4 Side lengths and angle measures in similar figures
- P.5 Similar triangles and indirect measurement
- P.6 Perimeters of similar figures
- P.7 Similarity rules for triangles
- P.8 Similar triangles and similarity transformations
- P.9 Similarity of circles
- P.10 Triangle Proportionality Theorem
- P.11 Areas of similar figures
- P.12 Prove similarity statements
- P.13 Prove proportions or angle congruences using similarity
- P.14 Proofs involving similarity in right triangles
- P.15 Prove the Pythagorean theorem
- Q.1 Pythagorean Theorem
- Q.2 Converse of the Pythagorean theorem
- Q.3 Pythagorean Inequality Theorems
- Q.4 Special right triangles
- R.1 Trigonometric ratios: sin, cos, and tan
- R.2 Trigonometric ratios: csc, sec, and cot
- R.3 Trigonometric ratios in similar right triangles
- R.4 Trigonometric functions of complementary angles
- R.5 Find trigonometric functions of special angles
- R.6 Find trigonometric functions using a calculator
- R.7 Inverses of trigonometric functions
- R.8 Trigonometric ratios: find a side length
- R.9 Trigonometric ratios: find an angle measure
- R.10 Solve a right triangle
- R.11 Law of Sines
- R.12 Law of Cosines
- R.13 Solve a triangle
- S.1 Perimeter
- S.2 Area of rectangles and squares
- S.3 Area of parallelograms and triangles
- S.4 Area of trapezoids
- S.5 Area and perimeter in the coordinate plane I
- S.6 Area and perimeter in the coordinate plane II
- S.7 Area and circumference of circles
- S.8 Area of compound figures
- S.9 Area between two shapes
- S.10 Area and perimeter of similar figures
- S.11 Heron's formula
- S.12 Area and perimeter mixed review
- T.1 Introduction to surface area and volume
- T.2 Surface area of prisms and cylinders
- T.3 Surface area of pyramids and cones
- T.4 Volume of prisms and cylinders
- T.5 Volume of pyramids and cones
- T.6 Surface area and volume of spheres
- T.7 Introduction to similar solids
- T.8 Surface area and volume of similar solids
- T.9 Surface area and volume review
- U.1 Parts of a circle
- U.2 Central angles
- U.3 Arc measure and arc length
- U.4 Area of sectors
- U.5 Circle measurements: mixed review
- U.6 Arcs and chords
- U.7 Tangent lines
- U.8 Perimeter of polygons with an inscribed circle
- U.9 Inscribed angles
- U.10 Angles in inscribed right triangles
- U.11 Angles in inscribed quadrilaterals I
- U.12 Angles in inscribed quadrilaterals II
- U.13 Construct a tangent line to a circle
- U.14 Construct an equilateral triangle inscribed in a circle
- U.15 Construct a square inscribed in a circle
- U.16 Construct a regular hexagon inscribed in a circle
- U.17 Construct the inscribed or circumscribed circle of a triangle
- V.1 Find the center of a circle
- V.2 Find the radius or diameter of a circle
- V.3 Write equations of circles in standard form from graphs
- V.4 Write equations of circles in standard form using properties
- V.5 Convert equations of circles from general to standard form
- V.6 Find properties of circles from equations in general form
- V.7 Graph circles from equations in standard form
- V.8 Graph circles from equations in general form
- W.6 Minimum and maximum area and volume
- W.8 Percent error: area and volume
- X.7 Geometric probability
- Y.1 Compass directions and vectors
- Y.2 Find the magnitude of a vector
- Y.3 Find the component form of a vector
- Y.4 Find the component form of a vector given its magnitude and direction angle
- Y.5 Graph a resultant vector using the triangle method
- Y.6 Graph a resultant vector using the parallelogram method
- Y.7 Add and subtract vectors

## Algebra 2 skills

- T.1 Identify the direction a parabola opens
- T.2 Find the vertex of a parabola
- T.3 Find the focus or directrix of a parabola
- T.4 Find the axis of symmetry of a parabola
- T.5 Write equations of parabolas in vertex form from graphs
- T.6 Write equations of parabolas in vertex form using properties
- T.7 Convert equations of parabolas from general to vertex form
- T.8 Find properties of a parabola from equations in general form
- T.9 Graph parabolas
- U.1 Find the center of a circle
- U.2 Find the radius or diameter of a circle
- U.3 Write equations of circles in standard form from graphs
- U.4 Write equations of circles in standard form using properties
- U.5 Convert equations of circles from general to standard form
- U.6 Find properties of circles from equations in general form
- U.7 Graph circles
- V.1 Find the center, vertices, or co-vertices of an ellipse
- V.2 Find the length of the major or minor axes of an ellipse
- V.3 Find the foci of an ellipse
- V.4 Write equations of ellipses in standard form from graphs
- V.5 Write equations of ellipses in standard form using properties
- V.6 Convert equations of ellipses from general to standard form
- V.7 Find properties of ellipses from equations in general form
- W.1 Find the center of a hyperbola
- W.2 Find the vertices of a hyperbola
- W.3 Find the length of the transverse or conjugate axes of a hyperbola
- W.4 Find the equations for the asymptotes of a hyperbola
- W.5 Find the foci of a hyperbola
- W.6 Write equations of hyperbolas in standard form from graphs
- W.7 Write equations of hyperbolas in standard form using properties
- W.8 Convert equations of hyperbolas from general to standard form
- W.9 Find properties of hyperbolas from equations in general form
- X.1 Convert between radians and degrees
- X.2 Radians and arc length
- X.5 Coterminal angles
- X.6 Reference angles
- Y.1 Pythagorean Theorem and its converse
- Y.2 Special right triangles
- Y.3 Trigonometric ratios: sin, cos, and tan
- Y.4 Trigonometric ratios: csc, sec, and cot
- Y.5 Trigonometric ratios in similar right triangles
- Y.6 Find trigonometric ratios using the unit circle
- Y.7 Sin, cos, and tan of special angles
- Y.9 Find trigonometric functions using a calculator
- Y.10 Inverses of sin, cos, and tan
- Y.12 Solve trigonometric equations I
- Y.13 Solve trigonometric equations II
- Y.14 Trigonometric ratios: find a side length
- Y.15 Trigonometric ratios: find an angle measure
- Y.16 Solve a right triangle
- Y.17 Law of Sines
- Y.18 Law of Cosines
- Y.19 Solve a triangle
- Y.20 Area of a triangle: sine formula
- Y.21 Area of a triangle: Law of Sines
- AA.1 Complementary angle identities
- AA.2 Symmetry and periodicity of trigonometric functions

## Precalculus skills

- M.1 Convert between radians and degrees
- M.2 Radians and arc length
- M.4 Coterminal and reference angles
- M.5 Find trigonometric ratios using right triangles
- M.6 Find trigonometric ratios using the unit circle
- M.8 Inverses of trigonometric functions
- M.9 Solve trigonometric equations
- M.10 Trigonometric ratios: find a side length
- M.11 Trigonometric ratios: find an angle measure
- M.12 Solve a right triangle
- M.13 Law of Sines
- M.14 Law of Cosines
- M.15 Solve a triangle
- M.16 Area of a triangle: sine formula
- M.17 Area of a triangle: Heron's formula
- O.1 Complementary angle identities
- O.2 Symmetry and periodicity of trigonometric functions
- P.1 Find properties of parabolas
- P.2 Write equations of parabolas in vertex form
- P.3 Graph parabolas
- P.4 Find properties of circles
- P.5 Write equations of circles in standard form
- P.6 Graph circles
- P.7 Find properties of ellipses
- P.8 Find the eccentricity of an ellipse
- P.9 Write equations of ellipses in standard form
- P.10 Find properties of hyperbolas
- P.11 Find the eccentricity of a hyperbola
- P.12 Write equations of hyperbolas in standard form
- P.13 Convert equations of conic sections from general to standard form
- S.8 Distance in the complex plane
- U.1 Find the magnitude of a vector
- U.2 Find the component form of a vector
- U.3 Find the direction angle of a vector
- U.4 Find the component form of a vector from its magnitude and direction angle
- U.5 Graph a resultant vector using the triangle method
- U.6 Graph a resultant vector using the parallelogram method
- U.7 Add and subtract vectors
- U.8 Find the magnitude and direction of a vector sum
- U.9 Multiply a vector by a scalar
- U.10 Find the magnitude of a vector scalar multiple
- U.11 Determine the direction of a vector scalar multiple
- U.12 Find a unit vector
- U.13 Linear combinations of vectors
- V.1 Find the magnitude of a three-dimensional vector
- V.2 Find the component form of a three-dimensional vector
- V.3 Add and subtract three-dimensional vectors
- V.4 Scalar multiples of three-dimensional vectors
- V.5 Find a three-dimensional unit vector
- V.6 Linear combinations of three-dimensional vectors