Exploring Similar Figures and Scale Drawings

What are the two conditions for two figures to be considered similar?

• Corresponding angles are equal and corresponding sides are equal.

• Corresponding angles are equal and corresponding sides form equal ratios.

• Corresponding angles are equal and the figures have the same perimeter.

• Corresponding sides are equal and the figures have the same area.

In similar triangles, if one side of the first triangle is 24 cm and the corresponding side of the second triangle is 30 cm, what is the ratio of the sides?

• 4:5

• 5:4

• 3:2

• 2:3

If triangle ABC is similar to triangle DEF and the sides of triangle ABC are 6 cm, 8 cm, and 10 cm, what is the length of the side corresponding to the 8 cm side in triangle DEF if the ratio of similarity is 2:1?

• 4 cm

• 16 cm

• 12 cm

• 8 cm

In similar trapezoids, if one side of the first trapezoid is 12 cm and the corresponding side of the second trapezoid is 6 cm, what is the ratio of the sides?

• 3:1

• 1:3

• 1:2

• 2:1

If the ratio of the sides of two similar trapezoids is 3:2 and one side of the first trapezoid is 15 cm, what is the length of the corresponding side in the second trapezoid?

• 10 cm

• 12 cm

• 9 cm

• 20 cm

A 6-foot-tall person casts a 4.5-foot shadow. If a flagpole casts a 15-foot shadow, how tall is the flagpole?

• 15 feet

• 18 feet

• 20 feet

• 10 feet

A 6-foot-tall person has a shadow that is 5 feet long. If a nearby tree has a shadow that is 30 feet long, what is the height of the tree?

• 40 feet

• 36 feet

• 30 feet

• 25 feet

What is a scale drawing?

• A drawing that is either enlarged or reduced but similar to the actual object.

• A drawing that is the same size as the actual object.

• A drawing that is larger than the actual object.

• A drawing that is smaller than the actual object.

If the scale of a map is 1 inch equals 100 miles, how many miles are represented by 1.5 inches on the map?

• 200 miles

• 100 miles

• 250 miles

• 150 miles

On a map with a scale of 1 inch equals 24 miles, how far apart are two cities that are 3 inches apart on the map?

• 120 miles

• 72 miles

• 96 miles

• 48 miles