The Total solution for NCERT class 6-12
ΔABC is an isosceles triangle in which AB = AC. Side BA isproduced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
In ΔABC,
AB = AC (Given)
⇒ ∠ACB = ∠ABC (Angles opposite to equal sides of atriangle are also equal)
In ΔACD,
AC = AD
⇒ ∠ADC = ∠ACD (Angles opposite to equal sides of atriangle are also equal)
In ΔBCD,
∠ABC + ∠BCD + ∠ADC = 180º(Angle sum property of a triangle)
⇒ ∠ACB + ∠ACB +∠ACD + ∠ACD = 180º
⇒ 2(∠ACB + ∠ACD) = 180º
⇒ 2(∠BCD) = 180º
⇒ ∠BCD = 90º