Question

prove that if each pair of opposite sides of a quadrilateral is equal ,then it is a parallelogram​

Answer 1

Given :

• AB = CD
• AD = BC
• ABCD is a parallelogram

To Prove :

• ∠DAC = ∠BCA
• ∠DCA = ∠BAC

Solution :

In Δ ADC and Δ BAC :-

$\longmapsto\tt{AB=CD (Given)}$

$\longmapsto\tt{BC=AD(Given)}$

$\longmapsto\tt{AC=AC(Common)}$

So, By SSS Rule ΔADC ≅ ΔABC..

Now :

$\longmapsto\tt{\angle{DAC}=\angle{BCA}(By\:CPCT\:Rule)}$

$\longmapsto\tt{\angle{DCA}=\angle{BAC}(By\:CPCT\:Rule)}$

Since ,Alternate Angles are Equal..So,

AB // CD

BC // AD

Hence , ABCD is a parallelogram..

━━━━━━━━━━━━━━━━━━━━

Properties of Parallelogram :

• Diagonals of parallelogram bisect each other.
• Opposite sides of parallelogram are congruent.
• Opposite angles of a parallelogram are also congruent.

━━━━━━━━━━━━━━━━━━━━