SOLUTION: Given: BD is perpendicular to AC and BD bisects AC Prove: Angle ABD and angle BCD are complementary angles

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Question 172860This question is from textbook GEOMETRY
: Given: BD is perpendicular to AC and BD bisects AC
Prove: Angle ABD and angle BCD are complementary angles This question is from textbook GEOMETRY

Answer by colliefan(242) About Me  (Show Source):
You can put this solution on YOUR website!
AD is congruent to DC because BD bisects AC
BD is a shared side of triangles BDA and BDC
angles ADB and CDB are both right angles and so are congruent
Triangles ADB and CDB are congruent by SAS
Angles CBD and ABD are congruent because these triangles are congruent
Angles CBD and BCD are conplementary because they are the acute angles in a right triangle
Angle ABD is then complementary to BCD because ABD and CBD are congruent