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 isosceles; Segment CD is the a
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 isosceles; Segment CD is the a
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Question 345593: 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 isosceles; Segment CD is the altitude to base of segment AB
TO PROVE:
Segment CD bisects angle ACB
Can someone PLEASE help me with this 2 column proof?
I have to put the statements and reasons....I am having so much trouble.
If CD is an altitude to AB, then CD must be perpendicular to AB because of the definition of an altitude. Since a ray perpendicular to a segment creates two right angles, angles ADC and BDC must both be right angles and therefore are equal in measure. Angles CAD and CBD must be equal in measure because the triangle is isosceles and AB is the base. Segment CD is equal in measure to segment CD since things are always equal to themselves. Hence triangle CAD is congruent to triangle CBD by AAS. Hence angle ACD is equal in measure to angle BCD by CPCT. Therefore segment CD bisects angle C by definition of an angle bisector.
John
My calculator said it, I believe it, that settles it
