Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

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

Back

It means that the ratios of the lengths of corresponding sides are equal.

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.

Front

What is the SSS criterion for triangle similarity?

Back

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

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 triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 6 (using the proportionality of sides).

Front

If the scale factor of two similar triangles is 3:2, what is the ratio of their areas?

Back

The ratio of their areas is 9:4 (the square of the scale factor).

Front

How do you find the length of a side in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides and solve for the unknown length.

Front

If triangle XYZ is similar to triangle PQR, and XY = 10 and PR = 15, what is the scale factor from triangle XYZ to triangle PQR?

Back

The scale factor is 1.5 (15/10).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.