Question

prove that the opposite side of a parrelogram are equal ​

Answer 1

Answer:

ABCD is a parallelogram.

To prove that AB = CD and AD = BC.

Join the diagonal AC.

In the triangles ABC and CDA:

angleBAC = angleDCA (alternate angles, AB || DC)

angleBCA = angleDAC (alternate angles, AD || BC)

AC = CA (common)

so triangleABC ≡ triangleCDA (AAS)

Hence AB = CD and BC = AD (matching sides of congruent triangles).

Answer 2

Correct Question :

Prove that the opposite sides of a parallelogram are equal .

Given :

• A parallelogram ABCD .

To Prove :

• AB = CD
• AD = BC

Solution :

In Δ ABC and Δ ADC :

$\longmapsto\tt{\angle{1}=\angle{4}\:(Alternate\:Angles)}$

$\longmapsto\tt{\angle{2}=\angle{3}\:(Alternate\:Angles)}$

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

So , By ASA Rule Δ ABC ≅ Δ ADC ..

Now ,

$\longmapsto\tt{AB=CD\:(By\:CPCT\:Rule)}$

$\longmapsto\tt{AD=BC\:(By\:CPCT\:Rule)}$

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Parallelogram :

A Quadrilateral which have opposite sides parallel and equal is called as Parallelogram .

Properties of Parallelogram :

• Opposite sides of parallelogram are equal .
• Opposite Angles of a parallelogram are equal .
• The diagonal of parallelogram bisects each other .

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