SOLUTION: ABC is an isosceles triangle with AB = AC . [FD] is drawn perpendicular to [BC] so it intersects [CA] at E, and the extension of [BA] at D. Show that triangle ADE is isosceles. Hin

Question 1191655: ABC is an isosceles triangle with AB = AC . [FD] is drawn perpendicular to [BC] so it intersects [CA] at E, and the extension of [BA] at D. Show that triangle ADE is isosceles. Hint: Start by letting hat CBA = alpha
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a diagram....

We are given AB = AC, so angles BCA and CBA are congruent. Let x be the measure each of those angles. Then...

(1) In triangle CFE, the measure of angle CEF is 90-x.
(2) in triangle BFD, the measure of angle BDF is 90-x.
(3) In triangle ADE, the measure of angle AED is 90-x, because it is a vertical angle with angle FEC.

So we have congruent angles ADE and ADE in triangle ADE; therefore triangle ADE is isosceles.

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