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Question

Prove two triangle congruent using a two column proof:

Given:AC is angle bisector of ∠BCD. m∠B = m∠D. Prove: ΔABC ≅ ΔADC

Statements:

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1. AC is angle bisector of angle BCD
2. angle 3 = angle 4
3. angle b = angle d
4. AC = AC
5. ΔABC ≅ ΔADC

https://drive.google.com/file/d/1kzVy5HeXz2ZDqv6PSXoXN1ld0NgtF8-X/view?usp=sharing

(^ link for triangle picture & etc.)

Answer 1

1) AC is GIVEN to be the angle bisector of angle BCD : GIVEN

2) angle 3 = angle BCA = angle ACD = angle 4 : def of equal angles

3) angle B = angle D is GIVEN

4) AC = AC by REFLEXIVE property

5) the triangles are congruent by AAS