Similar Figures

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 their corresponding sides are in proportion.

Front

What is the property of angles in similar figures?

Back

All corresponding angles in similar figures are congruent (equal in measure).

Front

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

Back

To set up a proportion, compare the ratios of corresponding sides of the similar figures. For example, if triangle ABC is similar to triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF).

Front

If a tree is 12 feet tall and casts a shadow 9 feet long, how tall is a building that casts a shadow 24 feet long?

Back

The building is 32 feet tall.

Front

What is the ratio of the sides of two similar triangles if one triangle has sides of 3, 4, and 5 and the other has sides of 6, 8, and 10?

Back

The ratio of the sides is 1:2.

Front

If triangle ABC is similar to triangle DEF and the length of side AB is 4 cm and side DE is 8 cm, what is the scale factor?

Back

The scale factor is 2.

Front

What is the missing side length if triangle GHI is similar to triangle JKL and the sides are in the ratio 3:5, with side GH measuring 9 cm?

Back

The missing side length JK is 15 cm.

Front

If two similar figures have a scale factor of 1:3, how does this affect their areas?

Back

The area of the larger figure is 9 times greater than the area of the smaller figure because area scales with the square of the scale factor (3^2 = 9).

Front

What is the missing side length in triangle DEF if it is similar to triangle XYZ and the sides are in the ratio 4:5, with side DE measuring 8 cm?

Back

The missing side length XY is 10 cm.

Front

If two similar rectangles have lengths of 4 cm and 8 cm, what is the ratio of their perimeters?

Back

The ratio of their perimeters is also 1:2.