Question

Triangle ABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD=AB. Show that angle BCD is an right angle

Answer 1

here is your solution..................

Answer 2

$\huge\underline\mathfrak{Answer:}$

AB = AC

$\angle$ACB = $\angle$ABC ............ 1.

AB = AD

•°• AC = AD

In ∆ADC, we have

AD = AC

$\angle$ACD = $\angle$ADC........... 2.

Adding (1) and (2), we have

$\angle$ACB + $\angle$ACD = $\angle$ABC + $\angle$ADC

$\implies$$\angle$BAC = $\angle$ABC + $\angle$ADC

Now, in ∆BCD, we have

$\angle$BCD + $\angle$ABC + $\angle$ADC = 180°.

$\implies$$\angle$BCD + $\angle$BCD = 180°.

$\implies$2$\angle$BCD= 180°.

$\implies$$\angle$BCD = 90°.