Similar Figures Using Proportions

Front

What are similar figures?

Back

Similar figures are shapes 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 does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.

Front

How do you determine if two figures are similar?

Back

To determine if two figures are similar, check if their corresponding angles are equal and if the ratios of the lengths of their corresponding sides are equal.

Front

What is the proportionality theorem?

Back

The proportionality theorem states that if two triangles are similar, the ratios of the lengths of their corresponding sides are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the ratio of their sides?

Back

The ratio of their sides is 1:2.

Front

If two similar triangles have a ratio of 3:5, and the shorter side of the first triangle is 9, what is the length of the corresponding side in the second triangle?

Back

The length of the corresponding side in the second triangle is 15.

Front

What is the scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of two corresponding sides of similar figures.

Front

If the scale factor of two similar triangles is 2:3, and the longer side of the first triangle is 12, what is the length of the corresponding side in the second triangle?

Back

The length of the corresponding side in the second triangle is 18.

Front

How do you solve for a missing side in similar figures?

Back

To solve for a missing side, set up a proportion using the lengths of the corresponding sides of the similar figures.

Front

If triangle XYZ is similar to triangle PQR, and XY = 10, PR = 15, what is the length of YZ if QR = 12?

Back

YZ = 8.