Deck 4: Triangles

Question 1

Given that , it follows that:

A)
B)
C)
D)

Answer 1

A

Question 2

Given that , it follows that .

Answer 2

False

Question 3

Given that P is the midpoint of and , what reason is used to establish that is congruent to ?

Answer 3

NOT ANSWERED.

Question 4

In the figure, and . If , , and , find the perimeter (the sum of lengths of all four sides)of quadrilateral XYZW .

Question 5

Which method for proving triangles congruent is used only for proving right triangles congruent?

Question 6

In order to justify the construction of the angle-bisector of , we verify that two triangles are congruent by which method?

A)SAS
B)ASA
C)SSS
D)HL

Question 7

In the figure, and bisects . Name the reason that justifies why .

Question 8

In for which , bisects . It follows that:

A) is a right triangle.
B)
C) is an equilateral triangle.
D)None of These

Question 9

Construction of an angle's bisector can be justified (proven)by showing that two triangles are congruent.

Question 10

The reason for the congruence of two triangles due to the congruence of two pairs of angles and their included pair of sides is represented by AAS.

Question 11

Suppose that you have utilized congruent vertical angles to prove that by the method SAS. By what reason can you, in turn, state that ?

A)Identity
B)SAS
C)CPCTC
D)Definition of midpoint

Question 12

The method CPCTC can be used to prove that two triangles are congruent.

Question 13

Given that and , which method establishes that ?

A)ASA
B)SAS
C)AAA
D)SSS

Question 14

Having proved that by the reason SSS, what reason allows you
to conclude that ?

Question 15

In a proof, what reason can be cited that justifies the statement ?

A)Symmetric Property of Congruence
B)Substitution Property of Equality
C)Transitive Property of Congruence
D)Identity

Question 16

The reason "Identity," which is used to state that a line segment or angle is congruent to itself, is also known as the Reflexive Property of Congruence.

Question 17

One of the methods for proving that two triangles are congruent is abbreviated AAA.

Question 18

Which three-letter symbol is used to indicate that two triangles are congruent becausetheir three pairs of sides are congruent?

Question 19

Which is NOT a method for proving two triangles congruent?

A)SSS
B)SSA
C)SAS
D)ASA

Question 20

You have proved that by the reason ASA and in turn that by CPCTC. What reason allows you to further conclude that " Z is the midpoint of ?"

Question 21

Where , and . Find .

Question 22

Given that is congruent to , , , and , find .

Question 23

In , . Which sides of must be congruent?

Question 24

Having proved that by SSS, we can then state that .

Question 25

In the figure, . If and , find .

Question 26

In the proof that , what statement can you justify by the reason Identity?

Question 27

Just as SSS, SAS, ASA, AAS, and HL are methods for proving that triangles are congruent, use three letters to state two methods that are not valid.

Question 28

For isosceles triangle XYZ with and point W on base , is an altitude. If XZ = 12 and YW = 8, find XY .

Question 29

In isosceles triangle RST , . If and , find the value of x .

A)x = 24
B)x = 32
C)x = 46
D)x = 58

Question 30

In the figure, the perpendicular-bisector of . If and , find WV .

Question 31

The bisector of one angle of a triangle always separates the triangle into two smaller and congruent triangles.

Question 32

If in , then .

Question 33

In the figure, the measure of exterior angle BCD is twice the measure of .What type of triangle is ?

Question 34

Given that point P is the midpoint of both and , it follows that .

Question 35

Given that is congruent to , , , , and ,find the perimeter .

Question 36

. In , is the median from vertex A to side . Likewise,
is the median of from vertex G to side . How are and related?

Question 37

If in , then .

Question 38

In the figure, bisects and D is the midpoint of . If and , find the value of x .

Question 39

Given that is congruent to , , and , find .

Question 40

In the figure, and bisect each other. If and is larger than , find .

Question 41

The perimeter P of an isosceles triangle with a leg of length a and base of length b is
given by .

Question 42

In the construction a regular hexagon, we constructed an exterior angle of the hexagon. What is the measure of each exterior angle of the regular hexagon?

A)30 °
B)45 °
C)60 °
D)None of These

Question 43

In the figure, A-C-D-B , , and . Of the line segments drawn from
point P to , which has the greatest length?

Question 44

In isosceles triangle RST , . If , , and the perimeter of is 36, find the value of x.

A)x = 5.5
B)x = 6
C)x = 6.5
D)None of These

Question 45

What part of is included by and ?

Question 46

To construct an angle that measures 60°, one begins by constructing perpendicular lines.

Question 47

In , it follows that

A) and include
B) and include
C) and include
D) and include

Question 48

In , . If AC = 6 and BC = 8, find AB .

A)10
B)12
C)14
D)None of These

Question 49

Two of the angles of a triangle have measures of 50° and 60°. Which number cannot be the measure of an exterior angle of this triangle?

A)100 °
B)110 °
C)120 °
D)130 °

Question 50

For the angle-measure indicated, which angle cannot be constructed?

A)22.5 °
B)30 °
C)40 °
D)45 °

Question 51

In (not shown), . Which statement is not necessarily true?

A)
B) is the vertex angle of
C) is the base of .
D) is the longest side of

Question 52

In , . Which statement is true?

A) is an altitude of .
B) is an altitude of .
C) is the longest side of .
D)The 3 angle-bisectors meet in the exterior of .

Question 53

If D is the midpoint of , what name is given to in relation to ?

A)angle-bisector
B)median
C)altitude
D)hypotenuse

Question 54

Where c is the length of the hypotenuse and a and b are the lengths of the legs, what equation relates these lengths?

Question 55

To construct the midpoint of the horizontal line segment , begin by marking off arcs of equal length from points A and B so that the arcs intersect both above and below .

Question 56

Given that is an obtuse triangle, it follows that:

A)the three angle-bisectors meet in the exterior of
B)the three medians meet in the exterior of
C)the three altitudes meet in the interior of
D)the 3 perpendicular-bisectors of the sides of meet in the exterior of the triangle

Question 57

If bisects of , then point D must be the midpoint of .

Question 58

Where a, b, and c are the lengths of sides, which triangle cannot be drawn?

A)a = 3, b = 4, c = 5
B)a = 3, b = 4, c = 6
C)a = 3, b = 4, c = 6.5
D)a = 3, b = 4, c = 7

Question 59

Find the measure of each interior angle of a regular polygon with 12 sides.

Question 60

In , the line segment joins vertex to point on the opposite side in such
a way that . In relation to , what name is given to ?

Question 61

In a right triangle, the side opposite the right angle is called the base of the right triangle.

Question 62

Given that the three sides of a triangle have measures of 5, 8, and x, find possible perimeters (P)of that triangle. Express the answer as an inequality.

Question 63

In right triangle ABC , . If and , find .

Question 64

When the 3 angle-bisectors of a triangle are constructed, what appears to happen?

Question 65

Suppose that bisects right angle ABC . In turn, bisects . Find .

Question 66

In where is a right angle, it follows that , and .

Question 67

To construct an isosceles triangle with vertex angle A and sides of length a, what arc would you draw first?

Question 68

In isosceles triangle RST with vertex angle S , . Describe the measure of .

Question 69

In , and . Name the longest side of .

Question 70

In the figure, bisects the acute angle of to form isosceles triangle ABD with base . Which side of is longest?

Question 71

In , . If , find .

Question 72

It is possible to draw a triangle whose sides measure 5 inches, 9 inches, and 14 inches.

Question 73

In a right triangle, the length of the hypotenuse is 13 inches and the length of one of the legs is 12 inches. Find the length of the other leg.

Question 74

The angle shown measures 60°. How would you construct an angle that measures 30°?

Question 75

In , and . If and , find the perimeter of .

Question 76

In the Pythagorean Theorem (where ), the number c represents the length of the hypotenuse of a right triangle.

Question 77

For , is an exterior angle. Which of the following must be true?

A)
B)
C)
D)

Question 78

has a perimeter of 84 cm. If cm and ST = 25 cm, find the angle of greatest measure in .

Question 79

For any real numbers a and b for which , there is a positive number p for which .