Question

Write a 2-column proof, without using the Angle Bisector Theorem, proving KL ≅ JK in the image below.

Answer 1

see below

Explanation:

We need to prove that KL ≅ JK .

Given :-

• Two right angled triangles ∆JKM and ∆LKM.

To prove:-

• KL ≅ JK

Proof:-

In ∆JKM and ∆LKM ,

• ang. KJM = ang. KLM = 90° (given )
• ang. LMK = ang. LMK
• KM = KM ( common )

Therefore by AAS congruence condition , ∆JKM ≅ ∆LKM .

Therefore,

• KL ≅ JK ( by cpct)

Hence proved !