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 length of a side in similar triangles?

Back

Use the proportion of corresponding sides. If triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.

Front

What is a proportion?

Back

An equation that states that two ratios are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 6, DE = 9, what is the ratio of their sides?

Back

The ratio is 6:9 or 2:3.

Front

How can you use similar triangles to find distances?

Back

By setting up proportions based on the corresponding sides of the triangles.

Front

What is the formula for finding the area of similar triangles?

Back

If the ratio of the sides of two similar triangles is a:b, then the ratio of their areas is a²:b².

Front

If two triangles have sides of lengths 4, 6, and 8, and 2, 3, and 4, are they similar?

Back

Yes, because the ratios of their corresponding sides are equal (4:2 = 6:3 = 8:4).

Front

What is the SSS criterion for similarity?

Back

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

Front

If two triangles are similar and the length of one side of the first triangle is 10 and the corresponding side of the second triangle is 15, what is the scale factor?

Back

The scale factor is 10:15 or 2:3.