Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the Angle-Angle (AA) criterion for similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the Side-Side-Side (SSS) criterion for similarity?

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the Side-Angle-Side (SAS) criterion for similarity?

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

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

Back

All corresponding angles are congruent.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 10 cm and side DE is 5 cm, what is the ratio of their corresponding sides?

Back

The ratio is 2:1.

Front

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

Back

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

Front

If the sides of triangle XYZ are 6 cm, 8 cm, and 10 cm, and triangle PQR is similar to triangle XYZ with a side length of 12 cm for side XY, what is the length of side PQ?

Back

The length of side PQ is 9 cm.

Front

What does it mean if two triangles are not similar?

Back

It means that their corresponding angles are not equal or their corresponding sides are not in proportion.

Front

How can you determine if two triangles are similar using a scale factor?

Back

If the lengths of corresponding sides have a constant ratio (scale factor), then the triangles are similar.