To prove two triangles congruent,
We can also use AAS criteria – Angle Angle Side
This criteria is equivalent to ASA Criteria.
Here’s how:
Suppose we are given two triangles Δ ABC & Δ PQR
Let’s prove this by ASA congruency finding ∠A & ∠P
In ∆ABC, |
In ∆PQR , |
By Angle Sum Property, ∠A + ∠B + ∠C = 180° ∠A + 40° + 80° = 180° ∠A + 120° = 180° ∠A = 180° − 120° ∠A = 60° |
By Angle Sum Property, ∠P + ∠Q + ∠R = 180° ∠P + 40° + 80° = 180° ∠P + 120° = 180° ∠P = 180° − 120° ∠P = 60° |
Now, In ∆ABC and ∆PQR,
∠A = ∠P (Both are 60°)
AC = PR (Given )
∠C = ∠R (Both are 80°)
∴ ∆ABC ≅ ∆PQR (ASA congruence rule)
OR
We can prove this by AAS
In ∆ABC and ∆PQR
∠B = ∠Q (Both are 40°)
∠C = ∠R (Both are 80°)
AC = PR ( Given )
∴ ∆ABC ≅ ∆PQR (AAS congruence rule)