Answer: d) Angle-Angle-Side (AAS)
Step-by-step 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).
