CONGRUENCE OF SIMPLE POLYGONS A1

Prove that the following triangle is isosceles.

Solution

Given: triangle LMN with M produced to X.

Required to prove: ∆LMN is isosceles

Proof: LX = XN (given)

<LXM = <MXN = 90⁰ (given)

MX = XM (common line)

∆LXM ≡ ∆NXM by SAS rule

ML = MN (Equal corresponding sides)

Hence ∆LMN is isosceles (proved)