Question

In a quadrilateral klmn kn=lm and angle knm=lmn. Prove that points k l m and n lie on circle

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Answer 1

Step-by-step explanation:

Heya!

Here is your answer!

Given: KLMN is a quadrilateral.

KN=LM, angle KNM = angle LMN.

To prove: That the quadrilateral is cyclic, i.e

All points lie on the circle.

Proof: Side KN = Side LM.......................{Given}

Therefore, opposite sides of the quadrilateral are equal.

Therefore, the quadrilateral KLMN is a Rectangle.

Now,

A quadrilateral is cyclic only when their opposite angles form 180°

But all angles of a rectangle are 90°

Therefore,

Angle KNM + Angle KLM

90° + 90°

180°

Therefore, quadrilateral KLMN is cyclic.

Therefore points K, L, M, N lie on the circle.