Triangle Similarity Practice Problems

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the Triangle Similarity Postulate?

Back

If two triangles have two pairs of corresponding angles that are equal, then the triangles are similar.

Front

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

Back

Use the proportion of the lengths of corresponding sides. If triangles ABC and DEF are similar, then \( \frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} \).

Front

What is a proportion in mathematics?

Back

An equation that states that two ratios are equal. For example, \( \frac{a}{b} = \frac{c}{d} \).

Front

How do you solve a proportion?

Back

Cross-multiply the terms and then solve for the unknown variable. For example, from \( \frac{a}{b} = \frac{c}{d} \), you get \( a \cdot d = b \cdot c \).

Front

What is the Scale Factor in similar triangles?

Back

The ratio of the lengths of corresponding sides of two similar triangles. It is constant for all corresponding sides.

Front

If triangle ABC is similar to triangle DEF, and AB = 6, DE = 9, what is the scale factor?

Back

The scale factor is \( \frac{AB}{DE} = \frac{6}{9} = \frac{2}{3} \).

Front

How do you set up a proportion to find a missing side?

Back

Set up the proportion using the lengths of the known sides of the similar triangles. For example, if \( \frac{AB}{DE} = \frac{BC}{EF} \), you can solve for the unknown side.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If \( \frac{8}{9} = \frac{w-2}{6} \), what is the value of w?

Back

Cross-multiply to get \( 8 \cdot 6 = 9(w - 2) \). This simplifies to \( 48 = 9w - 18 \), so \( w = \frac{66}{9} = \frac{22}{3} \).