Question

50 POINTS!!!!!!!!!!!

DETERMINE THE METHOD THAT VERIFIES IF THESE TRIANGLES ARE CONGRUENT.
Congruent: YES or NO ?
Congruency Statement: ∆ ABD ≅ ∆ ? Postulate: ?
(Postulates if the answer is yes: SSS, SAS, ASA, AAS, HL)
(Postulates if the answer is no: AAA, SSA)​

Answer 1

Congruent: YES

Congruency Statement: ∆ ABD ≅ ∆ DCA

Postulate: AAS postulate

Explanation:

To determine the method that verifies if the given triangles are congruent, we can look at the information and see which postulate applies.

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The information are as follows:

m ∠ ACD ≅ m ∠ ABD Given

m ∠ BAD ≅ m ∠ ADC (alternate interior angles)

AD = AD (common side)

This information corresponds to the AAS postulate, which states that two triangles are congruent if their corresponding angles and sides are congruent.

Therefore, the method that verifies if the given triangles are congruent is the AAS postulate.