Similarity Approaching Proficiency Practice

Front

What is the definition of similar figures?

Back

Similar figures are shapes 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 similarity statement for two similar triangles?

Back

The similarity statement for two similar triangles is written as ΔABC ~ ΔDEF, indicating that triangle ABC is similar to triangle DEF.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If the ratio of the sides of two similar triangles is 3:5, what is the ratio of their areas?

Back

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Therefore, (3:5)² = 9:25.

Front

How do you find the missing side in similar triangles?

Back

To find the missing side in similar triangles, set up a proportion using the lengths of the corresponding sides of the triangles.

Front

What is the formula for finding the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the length of the corresponding side of the other figure.

Front

If m∠A = 50° and m∠B = 50° in similar triangles, what can be inferred about m∠C?

Back

Since the triangles are similar, m∠C will also be equal to the corresponding angle in the other triangle.

Front

What is the relationship between the perimeters of two similar figures?

Back

The ratio of the perimeters of two similar figures is equal to the ratio of their corresponding sides.

Front

If a triangle has sides of lengths 6, 8, and 10, what is the scale factor if it is similar to a triangle with sides of lengths 9, 12, and 15?

Back

The scale factor is 3/2, as each side of the second triangle is 1.5 times the corresponding side of the first triangle.

Front

What is the definition of a proportion in the context of similar figures?

Back

A proportion is an equation that states that two ratios are equal, often used to compare the lengths of corresponding sides of similar figures.