Question 1

Given that  , it follows that:
A) 
B) 
C) 
D)

Accepted Answer

A

Question 2

Given that  , it follows that  .

Accepted Answer

False

Question 3

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

Accepted Answer

NOT ANSWERED.

Question 4

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

Accepted Answer

The answer of In the figure,  and  ....

Question 5

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

Accepted Answer

The answer of Which method for proving triangles congruent is...

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

Accepted Answer

The answer of In order to justify the construction of...

Question 7

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

Accepted Answer

The answer of In the figure,  and  bisects...

Question 8

In  for which  ,  bisects  . It follows that:
A)  is a right triangle.
B) 
C)  is an equilateral triangle.
D)None of These

Accepted Answer

The answer of In  for which  , ...

Question 9

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

Accepted Answer

Construction of an angle's bisector involves creating two congruent triangles by dividing the angle into two equal parts, and then using side-angle-side (SAS) congruence to show that the two resulting triangles are congruent. Therefore, the construction of an angle bisector can be justified through congruence.

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.

Accepted Answer

AAS (Angle-Angle-Side) is a valid congruence criterion for triangles. It states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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

Accepted Answer

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent. Since we have proven that the vertical angles of the two triangles are congruent, and we used SAS to prove congruence of one triangle, CPCTC allows us to conclude that the other sides and angles are also congruent, including the side and angle needed to show that the triangles are similar. Therefore, we can state that TBX8811 is similar to TBX8811.

Question 12

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

Accepted Answer

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. This means that if we can prove that all corresponding parts (sides and angles) of two triangles are congruent, then we have proven that the triangles themselves are congruent.

Question 13

Given that  and  , which method establishes that  ?
A)ASA
B)SAS
C)AAA
D)SSS

Accepted Answer

The answer of Given that  and  , which...

Question 14

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

Accepted Answer

The answer of Having proved that  by the reason...

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

Accepted Answer

The answer of In a proof, what reason can be...

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.

Accepted Answer

The Reflexive Property of Congruence states that any geometric figure is congruent to itself, including line segments and angles. Therefore, the reason "Identity" is also known as the Reflexive Property of Congruence is true.

Question 17

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

Accepted Answer

The AAA postulate (Angle-Angle-Angle) alone is not sufficient to prove that two triangles are congruent.

Question 18

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

Accepted Answer

The answer of Which three-letter symbol is used to indicate...

Question 19

Which is NOT a method for proving two triangles congruent?
A)SSS
B)SSA
C)SAS
D)ASA

Accepted Answer

The SSA (Side-Side-Angle) postulate is not a valid method for proving congruence as it can result in ambiguous cases.

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  ?"

Accepted Answer

The answer of You have proved that  by the...

Quiz 4: Triangles

Given that , it follows that:

Given that , it follows that .

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

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

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

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

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

In for which , bisects . It follows that:

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

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.

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

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

Given that and , which method establishes that ?

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

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

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.

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

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

Which is NOT a method for proving two triangles congruent?

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 ?"