Question

In Fig. 7.144, $\Delta ABC$ is right angled at C and $DE\perp AB$. Prove that $\Delta ABC\sim \Delta ADE$ and hence find the lengths of AE and DE.

Answer 1

Given ΔACB is right angled triangle and ∠C = ${90}^{\circ }$

We need to prove that ΔABC∼ΔADE and find the length of AE and DE.

∠A = ∠A (common angle)

∠C = ∠E (Both angles are equal to ${90}^{\circ }$

So, by AA similarity criterion,we have ΔABC∼ΔADE

Since, AB² = AC² + BC²

= 5² + 12²

= 13²
AB =13

In ΔABC∼ΔADE



DE = cm and AE = cm