Question

∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle.

Answer 1

In ∆ABC,

AB = AC (Given)

∠ACB = ∠ABC (Angles opposite to equal sides of a triangle are also equal)

In ∆ACD,

AC = AD

∠ADC = ∠ACD (Angles opposite to equal sides of a triangle are also equal)

In ∆BCD,

∠ABC + ∠BCD + ∠ADC = 180º (Angle sum property of a triangle)

∠ACB + ∠ACB + ∠ACD + ∠ACD = 180º

2( ∠ACB +∠ ACD) = 180º

2( ∠BCD) = 180º

∠BCD = 90º