SOLUTION: Theorem: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base of the triangle. Given:? To prove:? Analysis:? I have to proof by writing a

Algebra ->  Geometry-proofs -> SOLUTION: Theorem: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base of the triangle. Given:? To prove:? Analysis:? I have to proof by writing a       Log On


   

Question 86191: Theorem: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base of the triangle.
Given:?
To prove:?
Analysis:?
I have to proof by writing a statement and the reason for that statement.
Thank you
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
Given: Isosceles triangle ABC with AB congruent to AC [you draw]
AD bisects angle BAC [you draw ; endpoint D on base BC]
Prove: AD perpendicular to BC
1. Isosceles triangle ABC with AB congruent to AC 1. given
AD bisects angle BAC
2. angle BAD congruent to angle CAD 2. def. of angle bisector
3. AD congruent to AD 3. reflexive property
4. triangle BAD congruent to triangle CAD 4. SAS
5. angle BDA congruent to angle CDA 5. CPCTC
6. m angle BDA + m angle CDA = 180 6. linear pair postulate
7. m angle BDA = m angle CDA 7. def. congruent angles
8. m angle BDA + m angle BDA = 180 8. substitution
9. 2*m angle BDA = 180 9. substitution
10. m angle BDA = 90 10. division prop.
11. AD perpendicular to BC 11. def. perpendicular