Question

In the figure, $\text{DA}\perp \text{AB}$, $\text{CB}\perp \text{AB}$ and $\text{AC}=\text{BD}$. State the three pairs of equal parts in $\text{ΔABC}$ and $\text{ΔDAB}$. Which of the following statements is meaningful?
(i) $\text{ΔABC ≅ ΔBAD}$ (ii) $\text{ΔABC ≅ ΔABD}$

Answer 1

The three pairs of equal parts are:
$\text{∠ABC = ∠BAD}$ (= 90°)
$\text{AC = BD}$ (Given)
$\text{AB = BA}$ (Common side)

From the above, $\text{ΔABC ≅ ΔBAD}$ (By RHS congruence rule).
So, statement (i) is true.
Statement (ii) is not meaningful, in the sense that the correspondence among the vertices
is not satisfied.