Maths-

General

Easy

Question

# In the figure, OA = OD and OB = OC. Show that:

(i) AOB ⩭ DOC

(ii) AB || CD

Hint:

### Find the congruence rule used and then find the parallel sides.

## The correct answer is: AB || CD.

### (i) In ΔAOB and ΔDOC, we have

AO = OD (given)

BO = OC (given)

Since CB and AD intersects, we have

(vertically opposite angles)

So by SAS congruence rule, we have

ΔAOB ⩭ ΔDOC

(ii)Since ΔAOB ⩭ ΔDOC, we have

( Corresponding part of congruent triangles)

But they form alternate interior angles and since they are equal , AB || CD.

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