Answered

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A parallelogram with a diagonal drawn through it is shown below.



Arlen is trying to prove that RS ≅ TU, but is unable to come up with one of the lines of the proof.

STATEMENTS REASONS
RSUT is a parallelogram Given
∠RST ≅ ∠UTS and ∠RTS ≅ ∠UST If parallel lines are cut by a transversal, alternate interior angles are congruent.
ST ≅ ST Reflexive Property
ΔRST ≅ΔUTS ???
RS ≅ TU Corresponding parts of a congruent triangle are congruent.


What is the missing reason in the proof?

Sagot :

akposevictor

Arlen already established that ΔRST and ΔUTS has two pairs of congruent angles and a pair of congruent included sides, which meet the ASA Congruence Criterion. Therefore:

  • the missing statement in the proof is: ΔRST ≅ ΔUTS
  • the missing reason in the proof is: ASA Congruence Criterion

What is the ASA Congruence Criterion?

The ASA Congruence Criterion states that for two triangles to be considered congruent to each other, both triangles must have a pair of congruent included sides and two pairs of congruent angles.

Thus, the two-column proof that shows that RS ≅ TU that Arlen is trying to write, has already established that ΔRST and ΔUTS has the following:

Two pairs of congruent angles - ∠RST ≅ ∠UTS and ∠RTS ≅ ∠UST.

A pair of congruent included sides - ST ≅ S.

These satisfy the ASA Congruence Criterion. Therefore:

  • the missing statement in the proof is: ΔRST ≅ ΔUTS
  • the missing reason in the proof is: ASA Congruence Criterion

Learn more about the ASA Congruence Criterion on:

https://brainly.com/question/11637992

View image akposevictor
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