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In Figure, A B C D is a trapezium in whi...

In Figure, `A B C D` is a trapezium in which `A B || C D` and `A D=B C`. Show that :
(i) `/_A=/_B`
(ii) `/_C=/_D`
(iii) ` A B C~= B A D`
(iv) diagonal `A C=d i agon a lB D`

Text Solution

Verified by Experts

(i) Given,`AD = CE` (Opposite sides of parallelogram AECD)
Also, `AD = BC`
Therefore, `BC = CE`
`∠CEB = ∠CBE` (Angles opposite to equal sides in a triangle are equal)
`=>∠BAD + ∠CEB = 180°`
`=>∠BAD + ∠CBE = 180° ... (1)`
[Since, ∠CEB = ∠CBE]
Also,
...
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