Question

In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of $\angle BCD$?
(3 marks)

Answer 1

Given, AB = AC and AD = AB
$\Rightarrow AC=AD$ ( AC becomes the median of the triangle BCD)
(0.5 mark)

Now, as we know that angles opposite to equal sides are equal. Thus let, $\angle ABC=\angle ACB=x$
and, $\angle ADC=\angle ACD=y$
(0.5 mark)



$\text{Now, in}△BCD$
$x+y+x+y={180}^o$ (Angle sum property)
$\Rightarrow 2x+2y={180}^o$
$\Rightarrow x+y={90}^o$
$\Rightarrow \angle BCD={90}^o$
(2 marks)