Question

The proof that ΔABC ≅ ΔCDA is shown.

Given: ∥ and ∥
Prove: ΔABC ≅ ΔCDA



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. ?


A.perpendicular bisector theorem

B.Pythagorean theorem

C.HL theorem

D.SSS congruence theorem

Answer 1

it would be the sss congruence theorem

Answer 2

Answer: D. SSS congruence theorem

Explanation:

In the given proof we have in ΔABC ≅ ΔCDA

AB ≅ CD; BC ≅ DA [ opposite sides of a parallelogram are ≅]

AC ≅ AC [ reflexive property]

Therefore by SSS postulate of congruence ΔABC ≅ ΔCDA .

• The SSS postulate says that if all the three sides of a triangle is equal to all the three sides of another triangle then the triangles are said to be congruent.