CAT Important Theorem of Triangles - Practice Questions & MCQ

SAS Congruence Rule

Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

If ABC and PQR are two triangles, such that AB = PQ, BC = QR and ∠ABC = ∠PQR, then ∆ ABC ≅ ∆ PQR.

This result cannot be proved with the help of previously known results and so it is accepted true as an axiom  

ASA congruence rule

Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.

If ABC and PQR are two triangles, such that ∠BAC = ∠QPR and ∠ABC = ∠PQR and AB = PQ. It follows that ∆ ABC ≅ ∆PQR.

AAS congruence rule

In two triangles two pairs of angles and one pair of corresponding sides are equal but the side is not included between the corresponding equal pairs of angles. Then this triangle still congruent because as you know that the sum of the three angles of a triangle is 180°. So if two pairs of angles are equal, the third pair is also equal.

Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal. 

SSS congruence rule

If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

ABC and PQR are two triangles such that AB = PQ, BC = QR, and CA = RP, then ΔABC is congruent to ΔPQR.

We write this as ∆ ABC ≅ ∆ PQR.

RHS congruence rule

The RHS congruence property states that two right triangles are congruent if the hypotenuse and one side of a triangle are respectively equal to the hypotenuse and the corresponding side of the other right triangle.

In triangle ABC and triangle PQR, AB = PQ, AC = PR and ∠ABC = ∠PQR = (90°), then ∆ABC ≅ ∆PQR.