Asked by berlanda

The proof that ΔABC ≅ ΔCDA is shown.

Given: ∥ Line segment A B is parallel to line segment C D and Line segment B C is parallel to line segment D A ∥
Prove: ΔABC ≅ ΔCDA

Parallelogram A B C D is shown. A line is drawn from point A to point C to form 2 triangles.

What is the missing reason in the proof?

Statements Reasons
1. AB ∥ CD; BC ∥ DA 1. given
2. Quadrilateral ABCD is a ▱ 2. definition of parallelogram
3. AB ≅ CD; BC ≅ DA 3. opposite sides of a parallelogram are ≅
4. AC ≅ AC 4. reflexive property
5. ΔABC ≅ ΔCDA 5. ?
perpendicular bisector theorem
Pythagorean theorem
HL theorem
SSS congruence theorem

All Answers 1

Answered by GPT-5 mini AI
SSS congruence theorem.

Reason: AB = CD, BC = DA, and AC = AC (three pairs of corresponding sides equal), so ΔABC ≅ ΔCDA by SSS.