Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
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?
a. | 0.1 ft | c. | 1.6 ft | b. | 0.6 ft | d. | 2.5 ft |
|
|
|
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?  a. | 16 ft | b. | 14 ft | c. | 32 ft | d. | 12
ft |
|
|
|
5.
|
 has side lengths 5 cm, 7 cm, and 9 cm. If
 , which of the following could be the lengths
of the sides of  ? a. | 1 cm, 3 cm, 5 cm | b. | 6 cm, 8.4 cm, and 13.5 cm | c. | 7.5 cm, 10.5 cm,
13.5 cm | d. | 15 cm, 17 cm, and 19 cm |
|
|
|
6.
|
In the figure below,  and  .
The beginning of a proof is shown below. What is a valid reason for step 2?  Given:  Prove:  | Statements | Reasons | 1.  | Corresponding sides of similar
triangles are proportional. | 2.  | | | |
a. | Angle Addition Postulate | b. | Segment Addition Postulate | c. | Corresponding sides
of similar triangles are proportional. | d. | A midsegment in a triangle is parallel to one
side of the triangle and is half the length of that side. |
|
Short Answer
|
|
|
7.
|
 and AD = 7.5.
What is DC? Explain how you got your answer. 
|
|
|
8.
|
Are the two triangles (not drawn to scale) similar? If so, explain why they
are.  
|
|
|
9.
|
Are all regular hexagons similar? Explain.
|
|
|
10.
|
Which triangle below is not similar to any of the others? 
|
|
|
11.
|
Determine whether the triangles are similar. If the are, write a similarity
statement. 
|
|
|
12.
|
Determine whether the triangles are similar. If they are, write a similarity
statement. 
|
|
|
13.
|
In the figure below,  , with 
the image of  under a dilation with scale factor  . Write an expression for the perimeter of  in terms of the perimeter
of  . Explain your answer. 
|
|
|
14.
|
In the figure below,  .  a. Show  . b. Use the proportionality of sides of similar
triangles to solve for  . Then find the lengths of 
and  .
|
|
|
15.
|
Tell whether each pair of triangles is similar. Explain your reasoning. 
|
|
|
16.
|
|
|
|
17.
|
Given that  , explain why  . 
|
|
|
18.
|
Find the length of  .
|
Problem
|
|
|
19.
|
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. Show
that  . b. Use the
fact that corresponding sides of similar triangles are proportional to find  .
|