Question

ABCD is a trapezium in which AB is parallel to CD and AD is equal to BC. show that angle A is equal to angle B. angle C equal to angle D please give me answer I will mark as brainliest​

Answer 1

Required Question :

★ ABCD is a trapezium in which AB is parallel to CD and AD is equal to BC. show that angle A is equal to angle B. angle C equal to angle D ?

Concept :

• A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

• The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. A trapezium can also have parallel legs.

Given :

• ABCD is a trpazium where AB || CD and AD = BC.

To prove :

• ∠A = ∠B

Construction :

• Extend AB and draw a line through C parallel to DA intersecting AB produced at E.

Proof :

$\sf \: AD || CE \: - - - - \: ( \: From \: construction \: )$

$\sf \: and \: AE || DC \: - - - - \: (As \: AB || DC, \: and \: AB \: is \: extended)$

In AECD, both pair of opposite sides are parallel, AECD is a parallelogram.

Solution :

$\green{\sf∴ AD = CE - - - - \: (opposite \: sides \: of \: parallelogram \: are \: equal)}$

$\sf \: But \: AD = BC$

$\implies\sf BC = CE$

$\sf \: So, ∠CEB = ∠CBE - - - - \: (In \: ∆BCE, angle \: opposite \: to \: equal \: sides \: are \: equal) \: ...(1)$

$\small\sf \red {For \: AD || CE, and \: AE \: is \: the \: transversal }$

$\sf∠A + ∠CEB = 180°$

$\sf∠A = 180° - ∠CEB \: ...(2)$

Also AE is a line :-

$\sf \: So, ∠B + ∠CBE = 180° \: (linear \: pair)$

$\sf \: ∠B + ∠CBE = 180° - - - - [From \: (1) \: ]$

$\sf∠B = 180° - ∠CEB \: ... \: (3)$

$\sf \: From \: 2 \: and \: 3$

$\sf∠A = ∠B$

$\boxed{ \sf\red {{Hence, Proved}}}$

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✪ This question is from class 9th.

✪ Chapter / Name = 8 Quadrilaterals.

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Answer 2

Answer:

ABCD is a trapezium in which AB is parallel to CD and AD is equal to BC. show that angle A is equal to angle B. angle C equal to angle D

Step-by-step explanation