The proof is shown below:
What is congruency of Triangles?
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
In Δ PQR and ΔXYZ, as shown below, we can identify that PQ = XY, PR = XZ, and QR = YZ and ∠P = ∠X, ∠Q = ∠Y and ∠R = ∠Z. Then we can say that Δ PQR ≅ ΔXYZ.
What is ASA congruency criteria?
ASA criterion stands for Angle-Side-Angle criterion. Under the ASA criterion, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.
Given:
∠ACO ≅ ∠DBO, and BO ≅ CO
as, ∠COA =∠BOD (vertically opposite angles)
∠ACO ≅ ∠DBO ( given)
BO ≅ CO ( given)
So, By ASA (Angle-Side-Angle) congruency, △ACO ≅ △DBO
Learn more about congruency here:
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