Question

. If ABCD is a trapezium in which AB || CD and AD = BC, then:

a. ∠A = ∠B

b. ∠A > ∠B

c. ∠A < ∠B

d. None of the above
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Answer 1

Answer:

c. is the correct answer

Step-by-step explanation:

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Answer 2

Question:--

If ABCD is a trapezium in which AB || CD and AD = BC, then:

a. ∠A = ∠B

b. ∠A > ∠B

c. ∠A < ∠B

d. None of the above

Answer:--

Given:

ABCD is a trapezium where AB∣∣CD and AD=BC

Construction :

Extends AB and draw a line through C point to DA intersecting AB produced at E

Prrof: AD∣∣CE (from construction) &

AE∣∣DC (AS AB∣∣CD, & AB is extended)

AECD is a parallelogram.

In AECD, both pair of opposite sides are parallel.

∴AD=CE (opposite sides of parallelogram are equal)

But AD=BC (Given)

⇒BC=CE

So, ∠CEB=∠CBE ...(1) ( In ΔBCE, angles opposite to equal sides are equal)

For AD∣∣CE,

& AE is the transversal,

∠A+∠CEB=180°

[interior angles on same side of transversal is supplementary]

∠A=180°

-∠CEB ....(2)

Also AE is line,

so, ∠B+∠CE=180°

(liner pairs)

∠B+∠CBE=180° (from (1))

∠B=180° −∠CBE ....(3) (from (2) and (3)

∠A=∠B

∴ The answer is ∠A=∠B