Question

q1 :- proff that in a parallelogram opposite sides are equal​

Answer 1

$❍ \: \sf\bold{\red{Given :- }}$

A parallelogram ABCD

$❍\: \sf\bold{\red{ To \: proff :- }}$

(i) AB = DC

(ii) BC = AD

$❍ \: \sf\bold{\red{Construction :- }}$

Join AC

$❍ \: \sf\bold{\red{Proff :- }}$

In triangles ABC and CDA

Angle 1 = Angle 2 [ Alternate interior angles ]

Angle 3 = Angle 4 [ Alternate interior angles ]

AC = AC [ Common ]

∴ By ASA Congrency

Triangle ABC is congrent to Triangle CDA

∴ AB = CD [ C.P.C.T ]

BC = AD [ C.P.C.T ]

$❍ \: \sf\bold{\red{Note :- }}$

Figure in attachment

$❍\: \sf\bold{\red{ We \: know :- \: }}$

ASA Congruence Rule ( Angle – Side – Angle )

Two triangles are congruent if their corresponding two angles and one included side are equal .

Hope it helps you

Answer 2

Figure is in attachment

In a parallelogram opposite sides are equal

Given that

A Parallelogram ABCD

→Prove that

•)AB=CD

•) AD=BC

Let ABCD be a parallelogram

Then AB//CD(means AB parallel to BC)

Draw the diagonal AC

In ∆ABC and ∆ADC

AC=AC[Common side]

∠ACD=∠CAB[Pair of alternate angles]

∠DAC=∠ACB[Pair of alternate angles]

∆ABC≅∆ADC[ASA Congruent Theorem]

AB=CD and

AD=BC[Sides opposite to equal angles are equal]

ie,In a Parallelogram, opposite sides are equal.

Hope it helps you