Question

Given: AB ≅ CD and AD ≅ BC

Answer 1

Answer:

3rd answer

Step-by-step explanation:

Answer 2

Answer:

SSS congruency theorem ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the cases of congruent

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ  

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles  

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets complete the missing

- Given: AB ≅ CD and AD ≅ BC

- Prove: ABCD is a parallelogram

* Statements                         Reasons

1. AB ≅ CD ; AD ≅ BC         given

2. AC ≅ AC                           reflexive property  

3. △ ADC ≅ △ CBA             SSS congruency theorem

- The three sides in Δ ADC equal the three sides in ΔCBA,

  then the two triangles are congruent by SSS theorem

∴ The missing reason in step 3 is SSS congruency theorem