Question

Let ABC be an isosceles triangle at A. Take point D on side AC, point E on side AB such that AD = AE a) Compare the angles ABD and ACE b) Let I be the intersection of BD and CE. What kind of triangle is ΔIBC? Why ?

Answer 1

9514 1404 393

Answer:

a) they are congruent

b) isosceles; ∠IBC≅∠ICB

Explanation:

a) We are given that ΔABC is isosceles, such that AB≅AC. Points D and E are located so that AD≅AE. Of course, ∠A≅∠A, so ΔACE ≅ ΔABD by SAS. Then angles ABD and ACE are congruent by CPCTC.

__

b) Angle IBC is the difference between angle ABC and angle ABD. Angle ICB is the difference between angle ACB and angle ACE. These differences are between values that are the same, so the differences are the same. That means ∠IBC≅∠ICB, and ΔIBC is isosceles.