SAS Condition for Congruence

SAS Condition for Congruence

• SAS (Side-Angle-Side) Congruence Condition
• Verification of SSA (Side-Side-Angle) Condition
• Summary
• What’s Next?

In the previous segment, we saw Correspondence between Sides and Angles of Congruent Triangles. In this segment, we will learn some more conditions of congruence.

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SAS (Side – Angle – Side) Congruence Condition

This condition says that 2 triangles are congruent if 2 sides and the included angle of one triangle are respectively equal to the 2 sides and the included angle of the other triangle.

For example,

In △ABC and △PQR

Given: AB = PQ = 4 cm

BC = QR = 5 cm

m∠ABC = m∠PQR = 40°

Fig 1

Here, ∠ABC and ∠PQR are the included angles which are equal.

Also, the corresponding sides of both the triangles are equal.

Hence, △ABC ≅ △PQR by SAS congruence condition.

Can we determine congruence of two triangles by SSA (Side – Side

– Angle) Condition?

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