Triangle Inequality & Congruent Triangles Theorems

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| By Salhusseini
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Salhusseini
Community Contributor
Quizzes Created: 1 | Total Attempts: 471
Questions: 12 | Attempts: 471

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Triangle Inequality & Congruent Triangles Theorems - Quiz

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.                   


Questions and Answers
  • 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

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

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  • 2. 

    Refer to the figure. Complete the congruence statement 

    • A.

      Triangle VTU

    • B.

      Triangle TUV

    • C.

      Triangle VUT

    • D.

      Triangle UTV

    Correct Answer
    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.

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  • 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.

    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 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.

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  • 4. 

       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 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.

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  • 5. 

    • A.

      SAS Postulate

    • B.

      ASA Postulate

    • C.

      AAA Postulate

    • D.

      SSS Postulate

    Correct Answer
    A. SAS Postulate
  • 6. 

    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 (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.

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  • 7. 

    ΔSAM≅ΔRATWhich statement is NOT necessarily true?

    • A.

      MA = TA

    • B.

      MS = TR

    • C.

    • D.

    Correct Answer
    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.

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  • 8. 

    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 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.

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  • 9. 

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

    • A.

    • B.

    • C.

    • D.

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

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  • 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

    Correct Answer
    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.

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  • 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.

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  • 12. 

    The shortest side of ΔDEF is ___________.

    Explanation
    The shortest side of triangle ΔDEF is DE.

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