Similar Triangles Perimeter and Altitudes

If the ratio of the corresponding altitudes of two similar triangles is 2:3, and the area of the smaller triangle is 36 square units, what is the area of the larger triangle?

• 81

• 24

• 60

• 45

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

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.

What is the condition for two triangles to be similar using the side-side-side (SSS) similarity theorem?

• The area of the two triangles is the same

• The corresponding angles of the two triangles are equal

• The sum of the two sides of one triangle is equal to the sum of the two sides of the other triangle

• The corresponding sides of the two triangles are in the same ratio.

When two triangles are considered similar but not congruent?

• The distance between corresponding vertices are equal.

• The distance between corresponding vertices are proportionate.

• The vertices are reflected across the x-axis.

• Each of the vertices are shifted up by the same amount.

Given the diagram below, what is the value of x?

• 13.5

• 14.6

• 15.5

• 16.6

To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20 feet from the base of the lamppost. She then stepped back 4 feet so that she could see the top of the lamp post in the center of the mirror. Rachel's eyes are 5 feet 6 inches above the ground. What is the height, in feet, of the lamppost?

• 55 feet

• 27.5 feet

• 14.5 feet

• 7.27 feet

• 12.5

• 14.0

• 14.8

• 17.5

Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail?

• 15 ft

• 36 ft

• 60 ft

• 100 ft

The base of an isosceles triangle is 5 and its perimeter is 11. The base of a similar isosceles triangle is 10. What is the perimeter of the larger triangle?

• 15

• 21

• 22

• 110