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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (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.