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 does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle similarity. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side similarity. If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side similarity. 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.

Front

How can you determine if two triangles are not similar?

Back

If none of the conditions for AA~, SSS~, or SAS~ are met, the triangles are not similar.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding angles?

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

If the sides of triangle ABC are 3, 4, and 5, and the sides of triangle DEF are 6, 8, and 10, are the triangles similar?

Back

Yes, the triangles are similar by SSS~ because the sides are in proportion (3:6, 4:8, 5:10).

Front

What is the relationship between the areas of two 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 two triangles have a corresponding side ratio of 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

How do you find a missing side in similar triangles?

Back

Set up a proportion using the lengths of the corresponding sides of the similar triangles and solve for the missing side.