3. ASA Congruence

ASA Congruence

ASA Congruence Rule (Angle – Side – Angle )

The triangles are said to be congruent if two angles and the included side of a triangle are equal to two corresponding angles and the included side of another triangle.

Example :

Conclude that ∆AOC ≅ ∆BOD, using ASA congruence rule from the given figure.

Solution :

Consider the two triangles AOC and BOD,
Given that ∠C = ∠D =70°
Also, note that  ∠AOC = ∠BOD = 30° Which are vertically opposite angles
So, we can write that the angle A of triangle AOC
∆AOC = 180° – (70° + 30°) = 80° (By angle sum property of a triangle)
Similarly, for ∠B of ∆BOD = 180° – (70° + 30°) = 80°
So, we have ∠A = ∠B, AC = BD and ∠C = ∠D
Now, the side AC is between ∠A and ∠C and the side BD is between ∠B and ∠D.
So, by using ASA congruence rule, it is written as
∆AOC ≅ ∆BOD.