the legs of the smaller triangle to that of the larger triangle is 4 : 5. ... Given that solve for x and y. 4.) The triangles formed by two ladders le...
Chapter 8 Review 1.) Two American flags of difference dimensions are properly folded into two similar isosceles right triangles. The ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5. If the length of the hypotenuse of the larger triangle is 2 feet, what is the length of the hypotenuse of the small triangle to the nearest tenth of a foot?
2.) Given that
solve for x and y.
3.) One way to show that two triangles are similar is to show that ______. a. two angles of one are congruent to two angles of the other b. two sides of one are proportional to two sides of the other c. a side of one is congruent to a side of the other d. an angle of one is congruent to an angle of the other 4.) The triangles formed by two ladders leaning against a wall are similar. How far up the wall does the shorter ladder reach?
5.)
6.)
has side lengths 5 cm, 7 cm, and 9 cm. If
, which of the following could be the lengths of the sides of
and AD = 7.5. What is DC? Explain how you got your answer.
?
7.) Are the two triangles (not drawn to scale) similar? If so, explain why they are.
8.) Which triangle below is not similar to any of the others?
9.) Determine whether the triangles are similar. If they are, write a similarity statement.
10.) Determine whether the triangles are similar. If they are, write a similarity statement.
11.) In the figure below, .
Use the proportionality of sides of similar triangles to solve for . Then find the lengths of
and .
12.) Tell whether each pair of triangles is similar. Explain your reasoning.
13.) In and In similar, and if so, write a similarity statement.
14.) Given that ,
15.) Find the length of
and
State whether the triangles are
explain why .
.
16.) Andy wants to find the distance across a river. In order to find the distance , Andy stands at point , directly across from point , and walks 200 feet to the left, placing a marker at a point . Andy continues walking another 300 feet to point , and then follows the path to the left, walking until the markers at points and line up. Andy marks this location and measures .
a. b.
Show that . Use the fact that corresponding sides of similar triangles are proportional to find
.
17.) Find the value of x.
18.) Find KM
19.) The two gazebos shown are similar pentagons. Find the perimeter of Gazebo A.
20.) In the diagram, GHJK ~ LMNP. Find the area of LMNP. The area of GHJK = 84 m2
21.) A child who is 58 inches tall is standing next to a woman who is 5 feet 4 inches tall. The length of the woman’s shadow is 40 inches long. How long is the child’s shadow?
22.) Explain how to show that the indicated triangles are similar. a.)