$l$ is the perpendicular bisector of the line segment PQ and R is a point on the same side of $l$ as P. The line segment QR intersects $l$ at X. Prove that $P X + X R = Q R$ .

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Solution

Given X is point on perpendicular bisector of $P Q$ .
So, $P X = Q X$
Now, $P X + X R = Q X + X R$
Then, $P X + X R = Q R$

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l is the perpendicular bisector of the line segment PQ and R is a point on the same side of l as P. The line segment QR intersects l at X. Prove that PX+XR=QR.

Given X is point on perpendicular bisector of PQ.So, PX=QXNow, PX+XR=QX+XRThen, PX+XR=QR

$l$ is the perpendicular bisector of the line segment PQ and R is a point on the same side of $l$ as P. The line segment QR intersects $l$ at X. Prove that $P X + X R = Q R$ .

Given X is point on perpendicular bisector of $P Q$ .
So, $P X = Q X$
Now, $P X + X R = Q X + X R$
Then, $P X + X R = Q R$