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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
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:
