SOLUTION: In triangle ABC, D is the midpoint of base BC. If AD=BD=CD, find angle BAC with reasons.

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Question 1043918: In triangle ABC, D is the midpoint of base BC. If AD=BD=CD, find angle BAC with reasons.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Since D is the midpoint of BC, AD must be a perpendicular bisector of BC. Then angles ADB and ADC are right angles. Then triangles ADB and ADC are isosceles right triangles because AD = BD = CD. The acute angles of an isosceles right triangle measure 45 degrees. The angle measure you seek is then the sum of two 45 degree angles, that is the measure of angle BAC is 90 degrees.

To avoid confusion in the future, ask to find the MEASURE of an angle. Otherwise, I could correctly point to a diagram and say, "It's right there".

John

My calculator said it, I believe it, that settles it