ABCD is a trapezium in which AB ⃦CD and AD =BC (see the given figure). Show that
(i) ∠A = ∠B
(ii) ∠C=∠D
(iii) △ABC ≅△BAD
(iv) Diagonal AC=diagonal BD
[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

Open in App

Solution

We found a similar question to the one that you posted. Please check it out here.

Suggest Corrections

Similar questions

$A B C D$ is a trapezium in which $A B ∥ C D$ and $A D = B C$ show that
I) $∠ A = ∠ B$
II) $∠ C = ∠ D$
III) triangle $A B C$ congruent to triangle $B A D$
IV) diagonal $A C$ =diagonal $B D$

A B C D

is a trapezium in which

A B ∥ C D

and

A D = B C

(see figure). Show that
(i)

∠ A = ∠ B

(ii)

∠ C = ∠ D

(iii)

△ A B C \equiv △ B A D

(iv) diagonal

A C =

diagonal

B D

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.