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Need Help with this Geometry problem...

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2 column proof

Line segment MB is a median of triangle PMF, and line segment MP is congruent to line segment MF. How do you prove that segment MB is an angle bisector?


Consider triangles MBP and MBF.

The triangles share side MB - by construction.

BP is congruent with BF - because MB is a median and B is exactly in the middle of P and F

MP is congruent to MF - as stated in the problem


=> Triangles MBP and MBF are congruent.

=> angle PMB = angle FMB


angle PMF= angle PMB+ angle FMB = 2* angle PMB

=> MB is an angle bisector

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