Question

ABCD is a trapezium in which ab is parallel to CD and a b is equal to BC show that triangle ABC is congruent to triangle b a d​

Answer 1

Answer:

Step-by-step explanation:

its so simple yaar

as u know whts given

Constructions

Join AC and BD. Extend AB and draw a line through C parallel to DA meeting AB produced at E.

 = AE || DC …(1)  

and AD || CE …(2) [Construction]  

= ADCE is a parallelogram  

∠A + ∠E = 180' …(3) [Consecutive interior <'s [angle]]  

∠B + ∠CBE = 180' …(4) [Linear pair]  

AD = CE …(5) [Opposite sides of a ||gm]  

AD = BC …(6) [Given]  

= BC = CE [From (5) and (6)]  

= ∠E = ∠CBE …(7) [<'s opposite to equal sides]  

∴ ∠B + ∠E = 180' …(8)

[From (4) and (6)  

Now from (3) and (8) we have  

∠A + ∠E = ∠B + ∠E  

 ∴  ∠A = ∠B

now

In ∆ABC and ∆BAD, we have  

AD = BC [Given]  

∠A = ∠B [Proved]  

AB = CD [Common]  

 ∴∆ABC ≅ ∆BAD [ASA congruence rule ]

if u like it then let it b

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