Maths-

General

Easy

Question

# In the figure, AB = AC, and Then

- BC > CD
- BC = CD
- BC < CD
- cannot decide

## The correct answer is: BC = CD

### We should find relation between BC and CD

Given, AB = AC

$∠ABC=∠ACB=x$ (Isosceles triangle property)

In $△ABC$

$∠ABC+∠ACB+∠ABC=180$ (Sum of angles of triangle)

$x+x+48=180$

$2x=132$

$x=66_{∘}$

$∠BCA=∠BCD+∠DCB=66$

$∠BCD=66−18$

$∠BCD=48_{∘}$

Now, In $△BCD$

Sum of angles of triangle = 180

$∠BCD+∠BDC+∠DBC=180$

$48+∠BDC+66=180$

$∠BDC=66_{∘}$

Since, $∠BDC=∠DBC$

hence, $BD=CD$ (Isosceles triangle property)

Thus, $△BDC$ is an isosceles triangle.

Hence BC=CD

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