SOLUTION: Given: BM⊥AC , M is the midpoint of AC. Prove: ΔABM ≅ ΔCBM. Has to be written as Statements & Reasons. I really want to know how to do this!

Algebra ->  Geometry-proofs -> SOLUTION: Given: BM⊥AC , M is the midpoint of AC. Prove: ΔABM ≅ ΔCBM. Has to be written as Statements & Reasons. I really want to know how to do this!      Log On


   

Question 762957: Given: BM⊥AC , M is the midpoint of AC.
Prove: ΔABM ≅ ΔCBM.
Has to be written as Statements & Reasons. I really want to know how to do this!
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
This can be proved using the SAS (Side-Angle-Side) theorem, which is: If two corresponding sides, and the included angle, of 2 triangles are equal, then the 2 triangles are congruent.
If you compare triangles ABM and CBM,
Side MB is common to both.
AM = MC since M is the midpoint.
Angle AMB = angle BMC = 90, since BM is perpendicular to AC.
Hence 2 sides and the included angle are equal. So triangles ABM and CBM are congruent.
Hope this helps :)