Question

In Fig, DA ⊥ AB, CB ⊥ AB, and AC = BD. State the three pairs of equal parts in ∆ABC and ∆DAB. Which of the following statements is meaningful?

(i) ∆ABC ≅ ∆BAD
(ii) ∆ABC ≅ ∆ABD.

Answer 1

The three pairs of equal parts are:
∠ABC = ∠BAD...............( = 90°)
AC = BD...........................(Given)
AB = BA...........................(Common side)
From the above,
∆ABC ≅ ∆BAD..............(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.