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

Write a 2-column proof, without using the Angle Bisector Theorem, proving KL ≅ JK-example-1
User Boris Charpentier
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3.1k points

1 Answer

26 votes
26 votes

Answer:

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 !

User Monk
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2.6k points