Conditions for Congruent Triangles

09-07-202311-07-2023 app.cch No Comments

Three corresponding sides equal

Condition: $AB=PQ$, $BC=QR$ and $AC=PR$

Result: $\Delta ABC \cong \Delta PQR$

Reference: S.S.S.
Two corresponding sides equal and the included angle equals

Condition: $AB=PQ$, $BC=QR$ and $\angle B = \angle Q$

Result: $\Delta ABC \cong \Delta PQR$

Reference: S.A.S.
Two corresponding angles equal and the side between the two angles equal

Condition: $\angle B = \angle Q$, $\angle C = \angle R$ and $BC=QR$

Result: $\Delta ABC \cong \Delta PQR$

Reference: A.S.A.
Two corresponding angles equal and one corresponding side equals

Condition: $\angle A = \angle P$, $\angle B = \angle Q$ and $BC=QR$

Result: $\Delta ABC \cong \Delta PQR$

Reference: A.A.S.
For right-angled triangle, the hypotenuses equal and one corresponding side equals

Condition: $AB=PQ$, $AC=PR$ and $\angle C = \angle R = 90^\circ$

Result: $\Delta ABC \cong \Delta PQR$

Reference: R.H.S.

Math, Measures, Shape and Space, Revision Note, Triangles

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