Answer the Following:

Question

Given: Triangle ABC with median line AD is perpendicular to line BC

Prove in two column proof: Line AD bisects angle BAC and triangle ABC is isosceles

Answer 1

Triangle ABC with median line AD Given

perpendicular to line BC

ADC nd ADB are right angles Perpendicular lines form right angles

ADC and ADB are equal Right angles are congruent

AD = AD Reflexive property

DC = DB Definition of median

Triangle ADC and ADB are congruent SAS

AC = AB CPCTE

ABC is isosceles Definition of isosceles triangle (two sides equal)

<BAC = <DAC CPCTE

AD bisects <BAC Definition of angle bisector (divides angle into two equal parts)