Question

Angle XYZ is bisected by YP. L is any point on YP and MLN is perpendicular to YP. Prove that LM=LN.

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given: ∠XYZ is bisected by YP which means ∠XYP=∠ZYP, L is any point on YP and MLN is perpendicular to YP that is ∠YLM=∠YLN=90°.

To prove: LM=LN

Proof: In ΔMYL and ΔNYL, we have

∠YLM=∠YLN=90°( MLN is perpendicular to YP)

YL=YL( common)

∠MYL=∠NYL(Given)

Therefore, by ASA rule of congruency,

ΔMYL ≅ ΔNYL,

⇒By CPCTC, LM=LN

Hence proved.