Question

ABCD is a quadrilateral in which AB ‖ CD and AD = BC . Show that angle a = angle b​

Answer 1

Given :-

• ABCD is a Quadrilateral
• AB ‖ CD
• AD = BC

Construction :-

• Extend AB to E and draw a line CE parallel to AD

To Prove :-

• ∠A = ∠B

Explanation :-

➠ As AD ‖ EC and AE ‖ AC,

$\rm \boxed { \implies \bold { AECD \; is \; a \; Parallelogram }}$

➠ In Parallelogram AECD,

$\rm \implies AD = CE \qquad \bold{[Opposite \; side \; of \; Parallelogram]}$

$\rm \implies AD = BC \qquad \bold{[Given]}$

$\boxed { \rm \implies BC = CE } \qquad \bold{[From \; Above]}$

➠ In Triangle BCE,

$\rm \implies BC = CE \qquad \bold{[Proved]}$

$\boxed { \rm \implies \angle CBE = \angle CEB }$

➠ Now,

$\rm \implies \angle A \; + \; \angle CBE = 180^\circ \qquad \bold{[Angle \; on \; the \; same \; transversal \; and \; \angle CBE = \angle CEB]}$$\rm \implies \angle B \; + \; \angle CBE = 180^\circ \qquad \bold{[Linear \; Pair]}$

$\underline { \boxed { \bf \implies \angle A = \angle B }}$

Hence, In quadrilateral ABCD ; ∠A = ∠B

@Agamsain