Question

In given figure, can you use ASA congruence rule and conclude that $\text{ΔAOC ≅ ΔBOD}$?

Answer 1

In the two triangles $\text{AOC}$ and $\text{BOD}$,
$\text{∠C = ∠D}$ (each 70° )
Also, $\text{∠AOC = ∠BOD = 30°}$ (vertically opposite angles)

So, $\text{∠A}$ of $\text{AOC}=180°–(70°+30°)=80°$ (using angle sum property of a triangle)

Similarly, $\text{∠B}$ of $\text{BOD}=180°–(70°+30°)=80°$
Thus, we have $\text{∠A = ∠B, AC = BD}$ and $\text{∠C = ∠D}$
Now, side AC is between $\text{∠A}$ and $\text{∠C}$ and side $\text{BD}$ is between $\text{∠B}$ and $\text{∠D}$ .

So, by ASA congruence rule, $\text{ΔAOC ≅ ΔBOD}$.