Geometry

Explore angles, areas, shapes and the relationships between them.

Try a practice

Geometry

42° + 42° + 96° = 180°

Move the vertex

Angles

Use triangle sums, parallel lines and exterior angles. Move the diagram to explore the relationships.

1 comparison · 3 levels · Untimed

Geometry

½ × 6 × 4 = 12 square units

Change the height

Area

Compare triangle areas, rectangles and composite figures. Change dimensions to test your reasoning.

1 comparison · 3 levels · Untimed

Geometry

2× sides · 4× area

Scale the triangle

Triangles & shapes

Explore triangle inequalities, similar shapes and rhombus diagonals. Decide what follows from the givens.

1 comparison · 3 levels · Untimed

Geometry

Rise 1 ÷ run 3 = 1/3

Change the rise

Slopes

Compare rise and run, related lines and moving points. Explore how direction changes slope.

1 comparison · 3 levels · Untimed

Geometry

2× edge · 4× surface · 8× volume

Scale the cube

3D solids

Compare volume and surface area in cuboids, cylinders and cones. Explore what happens when a solid is scaled.

1 comparison · 3 levels · Untimed

Geometry

sin 30° ≈ 0.50 · cos 30° ≈ 0.87

Change the angle

Trigonometry

Compare right-triangle ratios, sine, cosine and tangent. Change the angle to explore their relationships.

1 comparison · 3 levels · Untimed

Geometry

90° rotation · lengths stay equal

Rotate the triangle

Transformations

Translate, reflect, rotate and scale figures. Explore what changes and what stays the same.

1 comparison · 3 levels · Untimed

Geometry

Midpoint (3, 2.5) · distance = 5

Move point B

Coordinate geometry

Use coordinates to compare distances, midpoints and moving points. Test relationships on a grid.

1 comparison · 3 levels · Untimed

Geometry

5 sides · 540° inside · 360° total turn

Change the number of sides

Polygons

Reason about interior angles, exterior turns and diagonals. Explore what regularity allows you to conclude.

1 comparison · 3 levels · Untimed

Geometry

1/4 of the circle · area 4π

Open the sector

Circle measures

Compare circumferences, areas, arcs and sectors. Change the radius or angle to test your reasoning.

1 comparison · 3 levels · Untimed

Area builder

Build connected shapes with a fixed area. Match a target perimeter, or find the smallest or largest possible perimeter.

1 puzzle · 3 levels · Untimed

Geometry

Gap 12. What is the radius?

Choose a number.

Circle geometry

Use tangent lines, circle centers and labeled measurements to find the radius that fits.

6 questions · 8 levels · 5 choices

Learn a method

Complete the angle sum

Find a missing triangle angle from the two angles you know.

4 min · Example and practice

Use base and height

Measure perpendicular height to compare triangle areas without relying on shape.

4 min · Example and practice

Count area and perimeter

Count filled unit squares for area and exposed edges for perimeter.

4 min · Example and practice

Scale similar triangles

Distinguish the scale factor for side lengths from the scale factor for area.

4 min · Example and practice

Read rise over run

Find a line’s slope from coordinate differences and keep the sign.

4 min · Example and practice

Scale length, area and volume

Predict how a solid changes when every length is multiplied by the same factor.

4 min · Example and practice

Connect the circle centers

Turn circle tangency into distances between centers, then use a right triangle to find a radius.

4 min · Example and practice

Follow circle tangency

Build equations from touching circles, then use the stated region to choose the circle that fits.

6 min · Example and practice

Choose a triangle ratio

Identify opposite, adjacent and hypotenuse before using sine, cosine or tangent.

4 min · Example and practice

Reason around the unit circle

Use coordinates, signs and identities to compare trigonometric expressions beyond a right triangle.

6 min · Example and practice

Track a transformation

Follow a rotation around a stated center and check what stays unchanged.

4 min · Example and practice

Use coordinate differences

Separate distance from midpoint by using differences for length and averages for location.

4 min · Example and practice

Sum polygon angles

Connect triangle totals to interior angles and one complete exterior turn.

4 min · Example and practice

Measure a circle sector

Use the central angle to take the same fraction of circumference or circle area.

4 min · Example and practice