Question

A student wants to prove that the diagonals of a parallelogram bisect each other. The student provides the diagram and proof below.

Given: Parallelogram GHJK with diagonals GJ¯¯¯¯¯ and HK¯¯¯¯¯¯ intersecting at L
Prove: GL¯¯¯¯¯≅JL¯¯¯¯¯ and HL¯¯¯¯¯≅KL¯¯¯¯¯

The student's proof is flawed. Which of the following statements explains why the proof is flawed?

A
Angles GHL and JKL are corresponding angles, not alternate interior angles.

B
Angles JLK and GLH are alternate interior angles, not vertical angles.

C
AAA is not an accepted triangle congruence criterion.

D
GL¯¯¯¯¯ corresponds to KL¯¯¯¯¯, not to JL¯¯¯¯¯, and HL¯¯¯¯¯ corresponds to JL¯¯¯¯¯, not to KL¯¯¯¯¯.

Answer 1

C. AAA is not an accepted triangle congruence criterion.

Explanation:

The proof is flawed because Angle-Angle-Angle is not an actual congruence rule, because this doesn't necessarily implies a congruence, it could also imply a similarity.

So, using the congruence between all three angles to demonstrate the congruence of two triangles is not right, because they could be similar and not congruent. The best way is to support the demonstration with postulate that involves congruence between sides, that way, they won't be room to flaws in the demonstration, because congruent sides imply congruent triangles.

Therefore, the right answer is C.

Answer 2

C AAA is not an accepted triangle congruence criterion

Explanation:

AAA can be used to show similarity, but not congruence. At least one side must be involved in any triangle congruence claim.

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The student could have made use of the fact that opposite sides are the same length, and used AAS or ASA to show congruence.