Question

traingle 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 angle RCD is a right angle. ABC is a right angled
:'(​

Answer 1

Given That:-

• AB = AC

• Also, AD = AB

• I.e. AC = AB = AD

To Prove:-

• ∠BCD = 90°

Proof:-

⇨∆ABC,

AB = AC

⇒∠ACB = ∠ABC (Angles Opposite To Equal Sides Are Equal ━ 2)

━━━━━━━━━━━━━━━━━━━

⇨In ∆ACD,

AC = AD

⇒∠ADC = ∠ACD (Angles Opposite To Equal Sides Are Equal ━ 1)

━━━━━━━━━━━━━━━━━━━

⇨In BCD,

➞ABC + ∠BCD + ∠BDC = 180° (Angles Sum Property Of Triangle)

➞∠ACB + ∠BCD + ∠ACD = 180° (From (1) & (2))

➞(∠ACB + ∠ACD) + ∠BCD = 180°

➞∠BCD + ∠BCD = 180°

➞2 ∠BCD = 180°

➞∠BCD = 180°/2

➞∠BCD = 90°

➷Hence Proved

━━━━━━━━━━━━━━━━━━━