Similar Figures

Front

What is the AA similarity theorem?

Back

The AA (Angle-Angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Front

What does it mean for two shapes to be similar?

Back

Two shapes are similar if they have the same shape but different sizes, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the SSS similarity theorem?

Back

The SSS (Side-Side-Side) similarity theorem states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is the SAS similarity theorem?

Back

The SAS (Side-Angle-Side) similarity theorem states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides.

Front

If the sides of two similar triangles are in the ratio 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 3²:5², which is 9:25.

Front

How do you find a missing side length in similar triangles?

Back

To find a missing side length in similar triangles, set up a proportion using the lengths of the corresponding sides.

Front

If triangle XYZ is similar to triangle PQR and the length of side XY is 6 cm and side PQ is 9 cm, what is the length of side YZ if side QR is 12 cm?

Back

Using the proportion, YZ = (6/9) * 12 = 8 cm.