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 triangle similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar (AA ~).

Front

What is the SSS criterion for triangle similarity?

Back

If the lengths of the corresponding sides of two triangles are in proportion, the triangles are similar (SSS ~).

Front

What is the SAS criterion for triangle similarity?

Back

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

Front

How do you find a missing side in similar triangles?

Back

Use the proportion of the corresponding sides. If triangle A has sides a, b, c and triangle B has sides x, y, z, then a/b = x/y.

Front

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

Back

The ratio of their sides is 1:2.

Front

Are triangles with angles 30°, 60°, and 90° similar to triangles with angles 30°, 60°, and 90°?

Back

Yes, they are similar by AA criterion.

Front

If two triangles have sides of lengths 3, 4, and 5, and 6, 8, and 10, are they similar?

Back

Yes, they are similar by SSS criterion.

Front

What does it mean if two triangles are not similar?

Back

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

Front

If triangle XYZ is not similar to triangle PQR, what can be concluded about their angles?

Back

At least one pair of corresponding angles is not equal.