Two triangles are necessarily congruent if and only if __________.

their corresponding sides and corresponding angles are congruent.

their corresponding angles are congruent.

their corresponding sides and corresponding angles are congruent, and they are rotated to the same position.

two of their sides are congruent.

Triangle Congruence Quiz 1

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| By Kslovich

Kslovich

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Quizzes Created: 1 | Total Attempts: 648

Questions: 12 | Attempts: 650 | Updated: Mar 21, 2023

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Questions and Answers

1.

How can you prove the triangles are congruent?
- A.
  
  SAS
- B.
  
  SSS
- C.
  
  ASA
- D.
  
  AAS
Correct Answer
A. SAS

Explanation
The SAS (Side-Angle-Side) congruence criterion states that if two triangles have two sides and the included angle of one triangle congruent to the corresponding parts of another triangle, then the triangles are congruent. In other words, if two triangles have two sides that are equal in length and the angle between them is also equal, then the triangles are congruent. This can be used as a proof to show that the given triangles are congruent.

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2.

How can you prove the triangles congruent?
- A.
  
  ASA
- B.
  
  AAS
- C.
  
  SAS
- D.
  
  SSS
Correct Answer
C. SAS

Explanation
SAS stands for Side-Angle-Side, which is a congruence postulate in geometry. It states that if two triangles have two sides and the included angle of one triangle congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In other words, if the lengths of two sides of a triangle and the measure of the angle between them are equal to the corresponding lengths and angle of another triangle, then the two triangles are congruent.

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3.

How can you prove the 2 triangles are congruent?
- A.
  
  ASA
- B.
  
  AAS
- C.
  
  SAS
- D.
  
  SSS
Correct Answer
D. SSS

Explanation
SSS stands for Side-Side-Side, which is a congruence postulate in geometry. It states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. In other words, if the lengths of all three sides of two triangles are equal, then the triangles are congruent. Therefore, if you can show that the lengths of all three sides of the two triangles are equal, you can prove that the triangles are congruent.

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4.

How can you prove the triangles are congruent?
- A.
  
  ASA
- B.
  
  AAS
- C.
  
  SAS
- D.
  
  SSS
Correct Answer
C. SAS

Explanation
SAS stands for Side-Angle-Side, which is a congruence postulate in geometry. It states that if two triangles have two sides and the included angle of one triangle congruent to the corresponding parts of another triangle, then the triangles are congruent. Therefore, if we have two triangles with a pair of congruent sides and the angle between them also congruent, we can prove that the triangles are congruent using the SAS postulate.

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5.

What else do you need to prove the triangles are congruent? Check all that apply
- A.
  
  Angle M = angle G
- B.
  
  Angle K = angle I
- C.
  
  Angle L = angle H
Correct Answer
C. Angle L = angle H

Explanation
To prove that the triangles are congruent, we need to show that all corresponding angles are equal. The given information states that angle L is equal to angle H, which satisfies one condition for congruence. However, we still need to prove that angle M is equal to angle G and angle K is equal to angle I in order to fully establish congruence.

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6.

How do you know the triangles are congurent?
- A.
  
  SSS
- B.
  
  SAS
- C.
  
  ASA
- D.
  
  HL
Correct Answer
B. SAS

Explanation
The triangles are congruent because the sides of one triangle are equal in length to the corresponding sides of the other triangle, and the included angle between those sides is equal in both triangles. This satisfies the SAS (Side-Angle-Side) congruence criterion.

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7.

Which combination of congruent corresponding parts can you not use to prove two triangles congruent?
- A.
  
  SAA
- B.
  
  AAA
- C.
  
  ASA
- D.
  
  SAS
- E.
  
  SSS
Correct Answer
B. AAA

Explanation
You remembered that you must have at least one pair of congruent sides.

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8.

Two triangles are necessarily congruent if and only if __________.
- A.
  
  Their corresponding angles are congruent.
- B.
  
  Their corresponding sides and corresponding angles are congruent, and they are rotated to the same position.
- C.
  
  Their corresponding sides and corresponding angles are congruent.
- D.
  
  Two of their sides are congruent.
Correct Answer
C. Their corresponding sides and corresponding angles are congruent.

Explanation
Two triangles are necessarily congruent if and only if their corresponding sides and corresponding angles are congruent. This means that not only do the lengths of the sides have to be equal, but the angles also have to be equal in order for the triangles to be congruent. This is a fundamental property of congruent triangles and is essential in determining whether two triangles are identical in shape and size.

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9.

by the _______________.
- A.
  
  SAS Postulate
- B.
  
  SSA Postulate
- C.
  
  SSS Postulate
- D.
  
  ASA Postulate
Correct Answer
C. SSS Postulate

Explanation
The SSS (Side-Side-Side) Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This means that all corresponding angles and sides of the triangles are equal in length. Therefore, the given answer, SSS Postulate, is the correct explanation for the question.

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10.
- A.
  
  SAS Postulate
- B.
  
  ASA Postulate
- C.
  
  AAA Postulate
- D.
  
  SSS Postulate
Correct Answer
A. SAS Postulate
11.

Which postulate or theorem shows that
- A.
  
  ASA Postulate
- B.
  
  SAS Postulate
- C.
  
  SSS Postulate
- D.
  
  AAS Theorem
Correct Answer
D. AAS Theorem

Explanation
The AAS theorem, or Angle-Angle-Side theorem, states that if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent. This theorem is used to prove congruence between triangles when given specific angle and side relationships.

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12.

By which reason can it be proven that triangles DAB and DAC are congruent?
- A.
  
  AAA
- B.
  
  AAS
- C.
  
  SSA
- D.
  
  SSS
Correct Answer
B. AAS

Explanation
The reason that can prove triangles DAB and DAC are congruent is AAS (Angle-Angle-Side). This is because the two triangles have two congruent angles (AAA) and a congruent side (A). According to the AAS congruence theorem, if two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent. Therefore, triangles DAB and DAC can be proven congruent using the AAS congruence criterion.

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