Question

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

Answer 1

construction: A line EF parallel to side AB OF parallelogram ABCD

proof: by mid point theorem prove EF PARALLEL TO AB AND EF PARALLEL TO CD.

then from the two equations formed prove AB PARALLEL TO CD

therefore opposite sides of parallelogram are equal.

Answer 2

Theorem : Opposite sides of a parallelogram are congruent.

Given : Quadrilateral ABCD is a parallelogram.

It means side AB side DC, side AD || side BC.

To prove : seg AD= seg BC ; seg DC = seg AB

Construction : Draw diagonal AC.

Proof :

seg DC || seg AB and diagonal AC is a transversal.

Angle DCA = Angle BAC (1)

and angle DAC = angle BCA (2) ......alternate angles

Now, in Triangle ADC and Triangle CBA,

DAC = BCA .... from (2)

DCA = BAC .... from (1)

seg AC E seg CA ......common side .

Triangle ADC = Triangle CBA...... ASA test

Therefore, side AD = side CB.... c.s.c.t.

and side DC= side AB ...... c.s.c.t.

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