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SAI International School

CLASS – VII

Mathematics

Chapter- 7: Congruence of Triangles-3
Lesson Notes - 3

SUBTOPICS: Criteria for congruence of triangles (ASA, RHS)

1) ASA Congruence criterion: If under a correspondence, two angles and the included
side of a triangle are equal to two corresponding angles and the included side of another
triangle, then the triangles are congruent.

EXAMPLE: In the given Figure, can you use ASA congruence rule and conclude that
∆AOC ≅ ∆BOD?

SOLUTION: 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.