Question

Prove that in a parallelogram, opposite sides are equal.​

Answer 1

Step-by-step explanation:

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Answer 2

Question:

Prove that in a parallelogram, opposite sides are equal.​

Given:

• ABCD is a parallelogram

• ∠B =∠D

• ∠A=∠C= $\frac{1}{2}\angle A=\frac{1}{2}\angle C$

To prove:

• AB = CD

• AD = BC

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

Solution:

ABCD is a parallelogram

∠B =∠D (Since opposite angles of a parallelogram are equal )

∠A=∠C= $\frac{1}{2}\angle A=\frac{1}{2}\angle C$ (Since opposite angles of a parallelogram are equal )

To prove AB = CD

AD=BC

Proof:

In ΔABC and ΔADC

• AC=AC (common side)

• ∠B =∠D (Given)

• $\frac{1}{2}\angle A=\frac{1}{2}\angle C$ ( Given)

By AAS congruency criterion,

ΔABC ≅ ΔADC

• AB = CD (By CPCT)

• BC = AD (By CPCT)

Answer:

• AB = CD (By CPCT)

• BC = AD (By CPCT)