Geometry: Triangles And Proving Triangles Congruent

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Geometry Quizzes & Trivia

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Questions and Answers
  • 1. 
    Given: In triangles ABC and XYZ, Angle A is congruent to angle X, side AB is congruent to side XY, and angle B is congruent to angle Y1. Prove: Triangle ABC is congruent to triangle XYZ2. Is the postulate you used valid? Does it work for any pair of triangles?
    • A. 

      1. AAS Theorem 2. Yes

    • B. 

      1. AAS Theorem 2. No

    • C. 

      1. ASA Postulate 2. Yes

    • D. 

      1. ASA Postulate 2. No

    • E. 

      1. SSA Postulate 2. No

  • 2. 
    Given: Side AB is congruent to side XY, side BC is congruent to side YZ, side AC is congruent to side XZ1. Do triangles ABC and XYZ have to be congruent based on the information above?2. If you said "No" to question #1, can triangles ABC and XYZ be congruent based on the information above?
    • A. 

      1. Yes 2. No, they HAVE to be congruent

    • B. 

      1. No 2. Yes

    • C. 

      1. No 2. No

    • D. 

      1. It depends on the type of triangle 2. Yes

  • 3. 
    Explain the HL Theorem.
    • A. 

      On a pair of right triangles, if two angles and a non-included side of the two triangles are congruent, then the triangles are congruent.

    • B. 

      On a pair of right triangles, if a leg of the right triangle (side touching the right angle) and the hypotenuse of the right triangle (side not touching the right angle) of two right triangles are congruent, then the triangles are congruent.

    • C. 

      If the height and length of two triangles are congruent, then the triangles are congruent.

    • D. 

      If two angles and two non-included sides of two triangles are congruent, then the triangles are congruent.

  • 4. 
    Given: Side AB is congruent to side XY, side BC is congruent to side YZ, angle C is congruent to angle ZAre triangles ABC and XYZ congruent?
    • A. 

      Yes, they have to be

    • B. 

      Nope.

    • C. 

      It depends on if angles C and Z are obtuse or acute

    • D. 

      Possibly