SOLUTION: Given: ∠BAD ≈ ∠CAD line AD perpendicular to line BC Prove Triangle ABC is isosceles

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Question 758773: Given: ∠BAD ≈ ∠CAD
line AD perpendicular to line BC
Prove Triangle ABC is isosceles
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Since given that is perpendicular to => angle degrees and angle degrees,

so angle is congruent to angle

The measure of angle is equal to minus minus the measure of angle ,
but since the measure of ,

the measure of angle is equal to minus minus the measure of angle

However, that is exactly the measure of angle .

Hence angle is congruent to angle .

Since , triangle is congruent to triangle by .
Then by , and finally is by .

or:

Given: AD perpendicular to BC; angle BAD congruent to CAD
Prove: ABC is isosceles

Proof:
statement..........................................reason
1. angle congruent to angle ..........................given
2. is perpendicular to , => is congruent to the angle ..........all right angles are congruent
3. is congruent to .......................... reflexive property
4. triangle congruent to triangle ...........by SAS
5. is congruent to ...................corresponding parts of congruent triangles are congruent
6. triangle is isosceles ....................it has two congruent sides


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