Deck 6: Similar Triangles

Question 1

. If , , , and , find DF .

A)12
B)15
C)16
D)18

Answer 1

D

Question 2

The notation SAS is used to prove that two triangles are congruent.

Answer 2

True

Question 3

In the proportion , the number b is known as the geometric mean for a and c .

Answer 3

False

Question 4

The owner and a partner in a small business share profits in the ratio 2:1. For a month in which the business realizes a profit of $15,600. what is the owner's share of the profit?

A)$5,200
B)$7,800
C)$10,400
D)None of These

Question 5

Write the acronym (the abbreviated form)for the statement, "Corresponding sides of similar triangles are proportional."

Question 6

Given that , it follows that .

Question 7

In the proportion , which numbers are the means?

Question 8

The measures of the three interior angles of are in the ratio 2:3:7. What type of triangle is ?

A)acute
B)right
C)obtuse
D)isosceles

Question 9

Solve the proportion for x .

A)
B)
C)
D)None of These

Question 10

Given that , the two triangles are similar. Which side of corresponds to side of the second triangle?

Question 11

What is the name of this property?
If , then .

Question 12

Any two squares are similar to each other.

Question 13

Suppose that you have proved that and , in turn, that . What reason would you use to further conclude that ?

Question 14

What does the question mark represent in this extended proportion?

Question 15

Given that quadrilateral quadrilateral MNPQ , .

Question 16

Any two polygons that are similar to each other are also congruent to each other.

Question 17

The most simplified form of the extended ratio 30° : 60° : 90° is 15 : 30 : 45.

Question 18

Quadrilateral ABCD quadrilateral HJKL . If , , , and , find x .

Question 19

In the figure, . What reason allows you to conclude that ?

Question 20

For two isosceles triangles, the vertex angles are congruent. How are the two triangles related?

Question 21

Given that , , , and , find PQ .

A)3
B)8
C)2.25
D)4.5

Question 22

In , and the length of the hypotenuse is 10. If one leg is twice as long as the other leg, find the length of the shorter leg. Express answer as a simplified square root.

Question 23

Given that , CSSTP leads to the extended proportion .

Question 24

In , one side has the length 5 inches and another side has length 12 inches. Find all possible lengths of the third side so that the triangle is a right triangle.

Question 25

In the figure, . If and , find the value of x .

A)65
B)75
C)85
D)None of These

Question 26

If  , then .

Question 27

Two sides of have lengths 5 inches and 6 inches. The length of the remaining and longest side is x inches. Determine all integer (whole number)values of x so that is an obtuse triangle.

Question 28

In rectangle ABCD , , , and . Find the value of x .

Question 29

The figure shows right triangle ABC with . Also, . Where , , , , and , what reason allows you to conclude that ?

Question 30

In isosceles triangle RST , . If , find the length of .

Question 31

Given that and , which method justifies that ?

A)AA
B)SAS
C)SAS
D)SSS

Question 32

The triple (20,21,29)is a Pythagorean Triple.

Question 33

If and , which method is used to prove that ?

A)AA
B)SAS
C)SAS
D)SSS

Question 34

In an equilateral triangle, each side measures 12 cm. Find the length of the altitude of this triangle.

Question 35

Each side of square MNPQ measures 8 inches. When the midpoints of the sides of the square are joined in order, quadrilateral HJKL is formed. What is the perimeter of HJKL?

Question 36

Given that , what angle of is congruent to of ?

Question 37

In the figure, and . What method allows you to conclude that ?

Question 38

If , then .

Question 39

In the figure, . If , , and , find QR .

Question 40

Which statement is true?

A)Any two equilateral triangles are similar.
B)Any two equilateral triangles are congruent.
C)Any two rectangles are similar.
D)Any two rectangles are congruent.

Question 41

In the figure, a bird (at point B)is 36 feet above the ground. Meg is 60 feet from the bird while Mara is 39 feet from the bird. How far apart are Meg and Mara?

A)60 feet
B)61 feet
C)63 feet
D)99 feet

Question 42

Where , , and , determine the Pythagorean Triple generated by and .

A)(45,28,53)
B)(47,53,56)
C)(10,18,28)
D)(20,21,29)

Question 43

The triangle with sides of lengths a = 4, b = 5, and c = 7 is an obtuse triangle.

Question 44

In the figure, . Also, , , and . Find TX .

Question 45

In a 30°-60°-90° right triangle with hypotenuse of length 12 inches, the shorter leg measures 6 inches.

Question 46

Which type of triangle has sides of lengths a = 8, b = 15, and c = 17?

A)acute
B)right
C)obtuse
D)No triangle with these lengths of sides exists.

Question 47

The triple (13,15,18)is a Pythagorean Triple.

Question 48

If and are divided proportionally at points M and N (as shown), then .

Question 49

In a 45°-45°-90° triangle, the length of a leg is the number a. What expression represents the length of the hypotenuse of this triangle?

Question 50

In , , , and . Considering sides and angles, what classification(s)of triangle are appropriate for ?

Question 51

In , and . If the length of is represented by 2 a , find an expression for the length of .

Question 52

In the legs of a right triangle are congruent, then the triangle is a 45°-45°-90° triangle.

Question 53

On a baseball diamond (a square), the distance from home plate to first base is 90 feet. Find the exact distance from home plate to second base.

A)90 feet
B) feet
C) feet
D)None of These

Question 54

In , and . If , find .

A)6
B)
C)
D)12

Question 55

In a 30°-60°-90° triangle, the hypotenuse has a length of 20 cm. Find the exact perimeter of this triangle.

A)
B)
C)
D)

Question 56

In the figure, . If , , , and ,
find the value of x .

Question 57

In , , , and . Which angle, if any, measures 90 ° ?

Question 58

In , . Also, . Find .

A)30 °
B)45 °
C)60 °
D)None of These

Question 59

Given that , , and in , it follows that .

Question 60

Given that (8,15,17)is a Pythagorean Triple, it follows that (24,45,c)is also a Pythagorean Triple. What is the value of c?

Question 61

In , bisects . If , , and , find XW .

A)3
B)3.3
C)3.5
D)4

Question 62

In the figure, . If , , and , find VZ .

A)4.75
B)5.75
C)8.75
D)None of These

Question 63

If bisects , then .

Question 64

The measures of two supplementary angles are in the ratio 2:3. Find the measure of the larger angle.

A)36 °
B)54 °
C)72 °
D)108 °

Question 65

For , intersects sides and so that . If and , what is the constant of proportionality k for the extended proportion ?

Question 66

For , . If , , and , find AS .

Question 67

In the figure, intersects two sides of as shown. If , what relationship must hold true?

Question 68

In the figure, bisects of . If , , and , find WZ .

Question 69

If in , then .

Question 70

Point D lies in the interior of . Line segments are drawn from vertices A , B , and C through point D to intersect at point E , at point F , and at point G . If , , , , and , find AG . [Hint: Use Ceva's Theorem.]

Question 71

For , . If , , and , find BC .

A)2
B)3
C)6
D)7.5