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