SOLUTION: Given: AD is the median to BC; AD is the altitude to BC Prove: Triangle ABC is isosceles

Question 826371: Given: AD is the median to BC; AD is the altitude to BC
Prove: Triangle ABC is isosceles
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If AD is the median to BC, D is the midpoint of BC.
If D is the midpoint of BC, BD=DC.
If AD is the altitude to BC, angles BDA and CDA are right angles.
So right triangles ABD and ACD have
congruent legs AD and BC,
congruent legs AD and AD,
and congruent angles ADb and ADC.
The two right triangles are congruent by SAS congruency
(two sides and the angle between them from one triangle, are congruent to corresponding parts in the other triangle.
Since Congruent Parts in Congruentr Triangles are Congruent (CPCTC),
hypotenuses AB and AC are congruent.
Since AB and AC are congruent, ABC is an isosceles triangle.
RELATED QUESTIONS
Given: ∠BAD ≈ ∠CAD line AD perpendicular to line BC Prove Triangle... (answered by MathLover1)

In triangle ABC, if altitude AD is drawn to side BC, which of the following must be... (answered by robertb)

GIVEN: D is the midpoint of line BC, line AD perpendicular to line BC PROVE: line AD... (answered by ikleyn)

Hi I am having trouble with an isosceles proof. I have triangle ABC. AD is... (answered by pedjajov)

In the figure if de||bc and ad=ae,then prove that abc is an isosceles... (answered by richard1234)

Given: Angle BAD ~ Angle CAD Underneath the ~ sign are equal marks AD congruent... (answered by solver91311)

How do I solve this with the given information? Given: angle BAD is about equal to angle (answered by richwmiller)

Given Angle BAD is congruent to Angle CAD AD is perpendicular to BC Prove that... (answered by richwmiller)

Given: Triangle ABC, AD bisects (answered by asuar010)