Solving 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 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

How do you find the missing length in similar triangles?

Back

Use the proportion of corresponding sides. If triangle A is similar to triangle B, then (side A1 / side B1) = (side A2 / side B2).

Front

If triangle ABC is similar to triangle DEF, and AB = 10, DE = 5, find the length of BC if EF = 2.5.

Back

BC = 5 (using the ratio 10:5 = BC:2.5).

Front

What is the SSS criterion for similarity?

Back

If the sides of one triangle are in proportion to the sides of another triangle, then the triangles are similar.

Front

What is the SAS criterion for similarity?

Back

If two sides of one triangle are in proportion to two sides of another triangle, and the included angles are equal, then the triangles are similar.

Front

If two triangles have sides in the ratio 3:4, what can be said about their angles?

Back

The angles of the triangles are equal, making them similar triangles.

Front

What is the relationship between the areas of similar triangles?

Back

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

Front

If triangle XYZ is similar to triangle PQR, and the ratio of XY to PQ is 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 4:9 (since (2^2):(3^2) = 4:9).

Front

What does it mean for sides to be corresponding in similar triangles?

Back

Corresponding sides are the sides that are in the same relative position in two similar triangles.