# Triangle Inequality & Congruent Triangles Theorems

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
| By Salhusseini
S
Salhusseini
Community Contributor
Quizzes Created: 1 | Total Attempts: 471
Questions: 12 | Attempts: 471

Settings

This will count as DOM # 1: Triangle Congruence.  You MUST show your final score to either Ms. A or Ms. MeGahee.  If you do not show either of us the score, you will receive a 0!  Good luck! You may use your notes / book.

• 1.

### 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

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

Rate this question:

• 2.

### Refer to the figure. Complete the congruence statement

• A.

Triangle VTU

• B.

Triangle TUV

• C.

Triangle VUT

• D.

Triangle UTV

C. Triangle VUT
Explanation
The correct answer is Triangle VUT because the vertices of the triangles are listed in a clockwise order. In congruence statements, the order of the vertices matters, and the given answer follows the correct order.

Rate this question:

• 3.

### 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.

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 is because congruent triangles have the same shape and size. The corresponding sides of congruent triangles are equal in length, and the corresponding angles are equal in measure. Therefore, if both the sides and angles of two triangles are congruent, then the triangles are necessarily congruent.

Rate this question:

• 4.

### by the _______________.

• A.

SAS Postulate

• B.

SSA Postulate

• C.

SSS Postulate

• D.

ASA Postulate

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 triangles are congruent. In other words, if all three sides of one triangle have the same length as the corresponding three sides of another triangle, then the two triangles are congruent. This postulate is used to determine congruence between triangles based solely on the lengths of their sides.

Rate this question:

• 5.
• A.

SAS Postulate

• B.

ASA Postulate

• C.

AAA Postulate

• D.

SSS Postulate

A. SAS Postulate
• 6.

### Which postulate or theorem shows that

• A.

ASA Postulate

• B.

SAS Postulate

• C.

SSS Postulate

• D.

AAS Theorem

D. AAS Theorem
Explanation
The AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent. This theorem is used to prove congruence between triangles when the given information involves two angles and a non-included side.

Rate this question:

• 7.

### ΔSAM≅ΔRATWhich statement is NOT necessarily true?

• A.

MA = TA

• B.

MS = TR

• C.

• D.

C.
Explanation
The statement "MA = TA" is not necessarily true. While it is given that ΔSAM is congruent to ΔRAT, it does not guarantee that the corresponding angles and sides are equal. Therefore, it is not necessary for the measure of angle MA to be equal to the measure of angle TA.

Rate this question:

• 8.

### By which reason can it be proven that triangles DAB and DAC are congruent?

• A.

AAA

• B.

AAS

• C.

SSA

• D.

SSS

B. AAS
Explanation
The reason why triangles DAB and DAC can be proven congruent is by using the AAS (Angle-Angle-Side) congruence criterion. This criterion 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 triangles are congruent. In this case, the two angles (AAA) are congruent, and the included side (side AD) is congruent. Therefore, by the AAS criterion, triangles DAB and DAC are congruent.

Rate this question:

• 9.

### Use the triangle inequality to determine the smallest angle in the figure.∠SCI

• A.

• B.

• C.

• D.

B.
Explanation
∠CIS. This angle is opposite from the smallest side. Therefore, according to the triangle inequality, it is the smallest angle.

Rate this question:

• 10.

### Which pair of triangles would you use ASA to prove the congruence of the 2 triangles?

• A.

A

• B.

B

• C.

C

• D.

D

B. B
Explanation
The triangles shown in choice C can be proven congruent by ASA. The triangles have 2 pairs of congruent angles and pair of congruent included sides.

Rate this question:

• 11.

### List the sides of the triangle in order from SHORTEST to LONGEST.

• A.

BA, BC, AC

Explanation
The sides of the triangle in order from shortest to longest are BA, BC, and AC.

Rate this question:

• 12.

### The shortest side of ΔDEF is ___________.

Explanation
The shortest side of triangle ΔDEF is DE.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

• Current Version
• Mar 19, 2023
Quiz Edited by
ProProfs Editorial Team
• Nov 17, 2009
Quiz Created by
Salhusseini

Related Topics