Similarity Problems

Use the information in the diagram to determine the height of the tree. Remember: lines with the same marks are congruent to each other.

• 80 feet

• 320 feet

• 40 feet

• 160 feet

A home's height is 40 ft. and casts a shadow that is 12 ft.. A car in the driveway is 10 ft. high. How long is the car's shadow?

• x = 3 ft.

• x = 12 ft.

• x = 120 ft.

• none of the above

A picture of a school’s mascot is 18 in. wide and 24 in. long. It is enlarged proportionally to banner size. If the width is enlarged to 63 in., what is the length of the banner?

• 84 in

• 71 in

• 47.25 in

• 80

If two triangles are similar, what can you say about their corresponding angles?

• Corresponding angles are supplementary

• Corresponding angles are equal

• Corresponding angles are parallel

• Corresponding angles are congruent

What is the ratio of the perimeters of two similar triangles?

• Difference of corresponding sides

• Sum of corresponding sides

• Product of corresponding sides

• Ratio of corresponding sides

In a similar figure, if one side of the first triangle is 5 cm and the corresponding side of the second triangle is 10 cm, what is the scale factor?

• 5

• 2

• 3

• 8

How do you determine if two triangles are similar using the side-angle-side (SAS) similarity theorem?

• Check if the corresponding sides are in the same ratio and the included angles are equal.

• Check if the corresponding sides are in different ratios and the included angles are equal.

• Check if the corresponding sides are in the same ratio and the included angles are different.

• Check if the corresponding sides are in the same ratio and the included angles are not equal.

If the ratio of the areas of two similar triangles is 4:9, and the area of the smaller triangle is 36 square units, what is the area of the larger triangle?

• 72

• 45

• 81

• 24

What is the relationship between the corresponding sides of similar triangles?

• They are parallel to each other

• They are equal in length

• They are in the same proportion or ratio.

• They are perpendicular to each other

How do you prove that two triangles are similar using the angle-angle (AA) similarity theorem?

• By showing that two corresponding angles of the triangles are congruent.

• By showing that the triangles have the same area.

• By showing that two corresponding sides of the triangles are congruent.

• By showing that the triangles have the same perimeter.