Question

State with triangle congruence postulate explain that the triangles are congruent​

Answer 1

Answer: d) Angle-Angle-Side (AAS)

Explanation:

See image --> I labeled the angles to show ΔABC and ΔCDE

Here is the proof that shows ΔABC ≡ ΔDEC

Statement Reason

1. AB ≡ DE 1. Given

2. ∠B ≡ ∠E 2. Given

3. ∠ACB ≡ ∠DCE 3. Vertical Angles

4. ΔABC ≡ ΔDEC 4. AAS Congruency Theorem

We have 2 angles and 1 side so our only options are AAS or ASA.

We can eliminate ASA because the side is NOT between the angles.

If you follow the path of the triangles; first you have Side (AB ≡ DE), then Angle (∠B ≡ ∠E), then Angle (∠ACB ≡ ∠DCE). We don't have SAA as an option so follow it backwards and you get Angle-Angle- Side (AAS).