Proof of Triangle KLM: PL=PK=PM & LKM = 90°

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In triangle KLM, with P as the midpoint of segment LM, the task is to prove that if PL = PK = PM, then angle LKM equals 90 degrees. The suggestion includes introducing point O to create line segment KPO, with P as the midpoint, and demonstrating that KLOM forms a rectangle. This approach leverages the properties of midpoints and rectangles to establish the right angle at K. The discussion emphasizes the geometric relationships and the need for a structured proof. Understanding these relationships is crucial for solving the problem effectively.
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here is a question that I need help with

1) In triangle KLM, P is the midpoint of the line segment LM. Prove that if PL = PK =PM, angle LKM = 90
L
|\
| \P
| \
|__ \
K M

If someone could set up the problem I'd be greatful
 
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Consider introducing a point O so that
KPO is a line segment with P at the midpoint, and then show that KLOM is a rectangle.
 
I think I got it now thanks for your help
 

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