Question

In Fig, can you use the ASA congruence rule and conclude that ∆AOC ≅ ∆BOD?

Answer 1

In the two triangles AOC and BOD, ∠C = ∠D..................(each 70° )

Also, ∠AOC = ∠BOD = 30°........................(vertically opposite angles)

So, ∠A of ∆AOC =180° – (70° + 30°) = 80°..................(using angle sum property of a triangle)

Similarly, ∠B of ∆BOD =180° – (70° + 30°) = 80°

Thus, we have ∠A =∠B, AC = BD, and ∠C = ∠D

Now, side AC is between ∠A and ∠C and side BD is between ∠B and ∠D.

So, by ASA congruence rule, ∆AOC ≅ ∆BOD.