SOLUTION: 2 column proof Given: angle BAD is congruent to angle CAD Line AD is Perpindicular to BC Prove: ABC is isosceles please help fast thanks!

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Question 284473: 2 column proof
Given: angle BAD is congruent to angle CAD
Line AD is Perpindicular to BC

Prove: ABC is isosceles
please help fast thanks!
Answer by solver91311(24713) About Me  (Show Source):
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Since AD is perpendicular to BC, angle ADC is right and angle ADB is right, so angle ADC is congruent to angle ADB. The measure of angle BAD is equal to 180 minus 90 minus the measure of angle ADB, but since the measure of ADB = the measure of ADC, the measure of angle BAD is equal to 180 minus 90 minus the measure of angle ADC. However, that is exactly the measure of angle CAD. Hence angle BAD is congruent to angle CAD. Since AD = AD, triangle ADC is congruent to triangle ADB by SAS. Then AB = AC by CPCT, and finally ABC is isosceles by definition.

John