Question

Prove that in any isosceles triangle, the median
drawn from the vertex angle is the perpendicular
bisector of the opposite side.

Answer 1

Given :Triangle ABC with AB = AC and median AD
Prove: AD is the perpendicular bisector of BC

1. AD is a median 1. Given
2. BD is congruent to CD 2. Definition of median
3. AD bisects BC 3. Definition of bisect
4. AD is congruent to AD 4. Reflexive
5. Triangle ABC is isosceles. 5. Given
6. AB is congruent to AC 6. Definition of isosceles triangle
7. Triangle ABD is congruent to triangle ACD 7. SSS
8. Angle ADB is congruent to angle ADC 8. CPCTC
9. m<ADB =m<ADC 9. Definition of congruent angles
10. m<ADB +m<ADC = 180 10. Definition of straight angle
11. 2m<ADB = 180 11. Substitution
12. m<ADB = 90 12. Division property of equality
13 AD is perpendicular to BC 13. Definition of Perpendicular