SOLUTION: Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is isoceles; Segment CD is the altit

Algebra ->  Geometry-proofs -> SOLUTION: Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is isoceles; Segment CD is the altit      Log On


   

Question 33947: Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: Triangle ABC is isoceles; Segment CD is the altitude to base Segment AB
To Prove: Segment CD bisects angle C
Plan: ??
Proof:??
I need to know what the plan would be and the proof, the statements and reasons.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: Triangle ABC is isoceles;
AC=CB
Segment CD is the altitude to base Segment AB...
WHERE D IS ON AB.
HENCE ANGLE CDA=90=ANGLE CDB
To Prove: Segment CD bisects angle C
THAT IS ANGLE DCA=ANGLE DCB
Plan: ??.
WE SHALL TRY TO PROVE BOTH TRIANGLES CDA AND CDB TO BE CONGRUENT
Proof:??
IN TRIANGLES CDA AND CDB WE HAVE
AC=CB........GIVEN
CD=CD......SAME COMMON SIDE
ANGLE CDA=90=ANGLE CDB........GIVEN
HENCE THE 2 TRIANGLES ARE CONGRUENT BY THEOREM ON CONGUENCE OF RIGHT TRIANGLES
HENCE ANGLE DCA=ANGLE DCB