Question

In the given figure, D is the mid-point of AB and $PC=\frac{1}{2}AP=3$ cm. If $AD=DB=4$ cm and $DE||BP$, then find the value of AE.
[2 marks]

Answer 1

Given∶ $\frac{1}{2}$ AP = 3 cm

$\therefore$ AP = 6 cm
[0.5 mark]

Now, D is mid-point and $DE||BP$

$\Rightarrow$ E is the mid-point of AP (Converse of mid-point theorem)
[0.5 mark]

$\therefore AE=\frac{1}{2}AP=\frac{1}{2}\times 6$ = 3 cm
[0.5 mark]

Hence, $AE$ = 3 cm
[0.5 mark]