Geometry skills

IXL has hundreds of Geometry skills to learn and review! As you work through a skill, questions will adapt to match your level. Keep answering questions to reach mastery!

A. Logic

1
Identify hypotheses and conclusions

2
Counterexamples

3
Conditionals

4
Negations

5
Converses, inverses, and contrapositives

6
Biconditionals

7
Truth tables

8
Truth values

B. Points, lines, line segments, and planes

1
Lines, line segments, and rays

2
Properties of planes, lines, and points

3
Describe intersections in a plane

4
Lengths of segments on number lines

5
Additive property of length

6
Midpoints

•
New! Weighted averages

7
Congruent line segments

8
Construct a congruent segment

9
Perpendicular Bisector Theorem

10
Midpoint formula: find the midpoint

11
Partition a line segment in a given ratio

12
Midpoint formula: find the endpoint

13
Distance formula

14
Distance to the origin in three dimensions

15
Construct the midpoint or perpendicular bisector of a segment

Checkpoint: Partition a line segment

C. Angles

1
Angle vocabulary

2
Angle measures

3
Identify complementary, supplementary, vertical, adjacent, and congruent angles

4
Find measures of complementary, supplementary, vertical, and adjacent angles

5
Angle diagrams: solve for the variable

6
Angle bisectors

7
Construct an angle bisector

8
Construct a congruent angle

9
Proofs involving angles

D. Parallel and perpendicular lines

1
Identify parallel, intersecting, and skew lines and planes

2
Construct a perpendicular line

3
Transversals: name angle pairs

4
Transversals of parallel lines: find angle measures

5
Transversals of parallel lines: solve for x

6
Construct parallel lines

7
Proofs involving parallel lines I

8
Proofs involving parallel lines II

Checkpoint: Definitions of geometric objects

Checkpoint: Line and angle theorems

E. Lines in the coordinate plane

1
Slopes of lines

2
Graph a linear equation

3
Equations of lines

4
Slopes of parallel and perpendicular lines

5
Equations of parallel and perpendicular lines

6
Find the distance between a point and a line

7
Find the distance between two parallel lines

Checkpoint: Coordinate proofs

Checkpoint: Parallel and perpendicular lines

F. Triangles review

1
Classify triangles

2
Triangle Angle-Sum Theorem

3
Exterior Angle Theorem

4
Exterior Angle Inequality

G. Polygons

1
Polygon vocabulary

2
Interior angles of polygons

3
Exterior angles of polygons

4
Interior and exterior angles of polygons: mixed practice

5
Construct an equilateral triangle or regular hexagon

6
Construct a square

H. Congruence transformations

1
Classify congruence transformations

2
Translations: graph the image

3
Translations: find the coordinates

4
Translations: write the rule

5
Reflections: graph the image

6
Reflections: find the coordinates

7
Rotate polygons about a point

8
Rotations: graph the image

9
Rotations: find the coordinates

10
Reflections and rotations: write the rule

11
Glide reflections: graph the image

12
Sequences of congruence transformations: graph the image

13
Sequences of congruence transformations: choose the sequence

14
Sequences of congruence transformations: find the rules

15
Transformations that carry a polygon onto itself

16
Congruence transformations: mixed review

Checkpoint: Congruence transformations

I. Dilations

1
Dilations: graph the image

2
Dilations: find the coordinates

3
Dilations: find length, perimeter, and area

4
Dilations: find the scale factor

•
New! Dilations: write the rule

5
Dilations: find the scale factor and center of the dilation

6
Dilations and parallel lines

Checkpoint: Transformations in the plane

Checkpoint: Dilations

J. Symmetry

1
Line symmetry

2
Rotational symmetry

3
Draw lines of symmetry

4
Count lines of symmetry

K. Congruent figures review

1
Congruence statements and corresponding parts

2
Solve problems involving corresponding parts

3
Identify congruent figures

4
Determine if two figures are congruent: justify your answer

L. Congruent triangles

1
Prove triangles are congruent using rigid motions

2
SSS and SAS Theorems

3
Proving triangles congruent by SSS and SAS

4
ASA and AAS Theorems

5
Proving triangles congruent by ASA and AAS

6
SSS, SAS, ASA, and AAS Theorems

7
SSS Theorem in the coordinate plane

8
Proving triangles congruent by SSS, SAS, ASA, and AAS

9
Proofs involving corresponding parts of congruent triangles

10
Congruency in isosceles and equilateral triangles

11
Proofs involving isosceles triangles

12
Hypotenuse-Leg Theorem

Checkpoint: Rigid motion and congruence

M. Similar figures

1
Ratios in similar figures

2
Similarity statements

3
Identify similar figures

4
Side lengths and angle measures in similar figures

5
Similar triangles and indirect measurement

6
Perimeters of similar figures

7
Angle-angle criterion for similar triangles

8
Similarity rules for triangles

9
Similar triangles and similarity transformations

10
Determine if two figures are similar: justify your answer

11
Similarity of circles

12
Triangle Proportionality Theorem

13
Similarity and altitudes in right triangles

14
Areas of similar figures

15
Prove similarity statements

16
Prove proportions or angle congruences using similarity

17
Proofs involving similarity in right triangles

Checkpoint: Similarity transformations

Checkpoint: Triangle similarity and congruence

Checkpoint: Prove circles are similar

N. Properties of triangles

1
Midsegments of triangles

2
Triangles and bisectors

3
Identify medians, altitudes, angle bisectors, and perpendicular bisectors

4
Angle-side relationships in triangles

5
Triangle Inequality Theorem

6
Construct the circumcenter or incenter of a triangle

7
Construct the centroid or orthocenter of a triangle

8
Find the centroid of a triangle

9
Proofs involving triangles I

10
Proofs involving triangles II

Checkpoint: Triangle theorems

O. Quadrilaterals

1
Identify trapezoids

2
Classify quadrilaterals I

3
Classify quadrilaterals II

4
Find missing angles in quadrilaterals

5
Graph quadrilaterals

6
Properties of parallelograms

7
Proving a quadrilateral is a parallelogram

8
Properties of rhombuses

9
Properties of squares and rectangles

10
Properties of trapezoids

11
Properties of kites

12
Properties of quadrilaterals: mixed practice

13
Classify shapes on the coordinate plane: justify your answer

14
Proofs involving triangles and quadrilaterals

15
Proofs involving quadrilaterals

Checkpoint: Parallelogram theorems

P. Pythagorean theorem

1
Pythagorean theorem

2
Prove the Pythagorean theorem

3
Converse of the Pythagorean theorem

4
Pythagorean Inequality Theorems

Q. Right triangle trigonometry

1
Trigonometric ratios: sin, cos, and tan

2
Trigonometric ratios with radicals: sin, cos, and tan

3
Trigonometric ratios: csc, sec, and cot

4
Trigonometric ratios in similar right triangles

5
Special right triangles

6
Find trigonometric functions of special angles

7
Solve a special right triangle

8
Find trigonometric functions using a calculator

9
Sine and cosine of complementary angles

10
Inverses of trigonometric functions

11
Trigonometric ratios: find a side length

12
Trigonometric ratios: find an angle measure

13
Solve a right triangle

•
New! Trigonometric ratios: word problems

Checkpoint: Right triangle trigonometry

R. Laws of Sines and Cosines

1
Law of Sines

2
Law of Cosines

3
Solve a triangle

4
Area of a triangle: sine formula

5
Area of a triangle: Law of Sines

Checkpoint: Laws of Sines and Cosines

S. Area and perimeter

1
Perimeter

2
Area of rectangles and squares

3
Area of parallelograms and triangles

4
Area of trapezoids

5
Area of rhombuses

6
Area of regular polygons

7
Area and perimeter in the coordinate plane I

8
Area and perimeter in the coordinate plane II

9
Area and circumference of circles

10
Area of compound figures

11
Area between two shapes

12
Area and perimeter of similar figures

13
Perimeter and area: changes in scale

14
Heron's formula

15
Area and perimeter mixed review

Checkpoint: Area and perimeter in the coordinate plane

T. Three-dimensional figures

1
Parts of three-dimensional figures

2
Three-dimensional figure vocabulary

3
Nets and drawings of three-dimensional figures

4
Cross sections of three-dimensional figures

5
Solids of revolution

Checkpoint: Cross sections and solids of revolution

U. Surface area and volume

1
Lateral area of prisms and cylinders

2
Lateral area of pyramids and cones

3
Surface area and volume of rectangular prisms

4
Surface area of prisms and cylinders

5
Surface area of pyramids and cones

6
Surface area of spheres

7
Volume of prisms and cylinders

8
Volume of pyramids and cones

9
Volume of spheres

10
Volume of compound figures

11
Similar solids: find the missing length

12
Surface area and volume of similar solids

13
Surface area and volume: changes in scale

14
Perimeter, area, and volume: changes in scale

15
Surface area and volume review

Checkpoint: Surface area

Checkpoint: Volume

V. Measurement

1
Convert rates and measurements: customary units

2
Convert rates and measurements: metric units

3
Convert square and cubic units of length

4
Precision

5
Greatest possible error

6
Minimum and maximum area and volume

7
Percent error

8
Percent error: area and volume

9
Calculate density, mass, and volume

Checkpoint: Geometric modeling and design

Checkpoint: Density

W. Circles

1
Parts of a circle

2
Central angles and arc measures

3
Understand arc length and sector area of a circle

4
Arc length

5
Convert between radians and degrees

6
Radians and arc length

7
Area of sectors

8
Circle measurements: mixed review

9
Arcs and chords

10
Tangent lines

11
Perimeter of polygons with an inscribed circle

12
Inscribed angles

13
Angles in inscribed right triangles

14
Angles in inscribed quadrilaterals I

15
Angles in inscribed quadrilaterals II

16
Angles formed by chords, secants, and tangents

17
Segments formed by chords, secants, and tangents

Checkpoint: Angles and lines in circles

Checkpoint: Inscribed and circumscribed circles

Checkpoint: Arc length and area of sectors

X. Constructions with circles

1
Construct a tangent line to a circle

2
Construct an equilateral triangle inscribed in a circle

3
Construct a square inscribed in a circle

4
Construct a regular hexagon inscribed in a circle

5
Construct the inscribed or circumscribed circle of a triangle

Checkpoint: Geometric constructions

Y. Circles in the coordinate plane

1
Find the center of a circle

2
Find the radius or diameter of a circle

3
Determine if a point lies on a circle

4
Derive equations of circles using the Pythagorean theorem

5
Write equations of circles in standard form from graphs

6
Write equations of circles in standard form using properties

7
Convert equations of circles from general to standard form

8
Find properties of circles from equations in general form

9
Graph circles from equations in standard form

10
Graph circles from equations in general form

Checkpoint: Equations of circles

Z. Parabolas in the coordinate plane

1
Find the vertex of a parabola

2
Find the focus or directrix of a parabola

3
Find the axis of symmetry of a parabola

4
Write equations of parabolas in vertex form from graphs

5
Write equations of parabolas in vertex form using the focus and directrix

6
Write equations of parabolas in vertex form using properties

7
Convert equations of parabolas from general to vertex form

8
Find properties of a parabola from equations in general form

9
Graph parabolas

Checkpoint: Equations of parabolas

AA. Probability

1
Theoretical and experimental probability

2
Outcomes of compound events

3
Identify independent and dependent events

4
Probability of independent and dependent events

5
Counting principle

6
Permutations

7
Permutation and combination notation

8
Find probabilities using combinations and permutations

9
Find probabilities using two-way frequency tables

10
Identify independent events

11
Find conditional probabilities

12
Find conditional probabilities using two-way frequency tables

13
Independence and conditional probability

14
Geometric probability

15
Find probabilities using the addition rule

Checkpoint: Understand independence and conditional probability

Checkpoint: Probabilities of compound events

BB. Vectors

1
Compass directions and vectors

2
Find the magnitude of a vector

3
Find the component form of a vector

4
Find the component form of a vector given its magnitude and direction angle

5
Graph a resultant vector using the triangle method

6
Graph a resultant vector using the parallelogram method

7
Add vectors

8
Subtract vectors