Examples: Congruence of Triangles All Criteria- 2 Video Lecture | Mathematics for Year 8

Ans. The criteria for congruence of triangles are: 1. Side-Side-Side (SSS) criterion: If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. 2. Side-Angle-Side (SAS) criterion: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. 3. Angle-Side-Angle (ASA) criterion: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. 4. Angle-Angle-Side (AAS) criterion: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Ans. To prove that two triangles are congruent using the SSS criterion, you need to show that all three sides of one triangle are congruent to the corresponding sides of the other triangle. You can do this by measuring the lengths of the sides and showing that they are equal. Alternatively, you can use other known information, such as congruent angles, to deduce that the sides are congruent.

Ans. No, two triangles cannot be congruent if only their angles are equal. In order for triangles to be congruent, their corresponding sides and angles must be equal. Having equal angles alone is not sufficient to prove congruence. The side lengths must also be equal or satisfy one of the other criteria for congruence, such as the SSS, SAS, ASA, or AAS criterion.

Ans. Yes, it is possible for two triangles to have equal side lengths but different angles. The congruence of triangles is determined by the equality of both side lengths and angles. If the side lengths are equal but the angles are different, the triangles would not be congruent. Congruence requires the equality of corresponding sides and angles.

Ans. To prove that two triangles are congruent using the SAS criterion, you need to show that two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of the other triangle. You can do this by measuring the lengths of the sides and the angles and showing that they are equal. Alternatively, you can use other known information, such as congruent angles or side lengths, to deduce the congruence using the SAS criterion.