Question

20
** 4 marks each **
(a) ABCD is a trapezium in which AB // CD
and AD = BC (See
figure). Show that:
(0) ZA = LB
(ii) ZC = ZD
(iii) A ABC « A BAD
(iv) Diagonal AC = Diagonal BD
(b) Prove that angles opposite to equal sides
in an
isosceles triangle are equal.
(Non-anonymous question )*
(8 Points)
A
B
D​

Answer 1

Answer:

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Answer 2

Answer:

(b)

Let △ABC be an isosceles triangle such that AB =AC Then we have to prove that ∠B=∠C Draw the bisector AD of ∠A meeting BC in D

Now in triangles ABD and ACD We have AB=AC (Given)

∠BAD=∠CAD (because AD is bisector of ∠A

AD=AD (Common side)

Therefore by SAS congruence condition we have

△ABC≅△ACD

⇒∠B=∠C

(Corresponding parts of congruent triangles are equal )