Examples: Congruence of Triangles All Criteria- 1 Video Lecture | Mathematics for Year 8

Ans. The different criteria for congruence of triangles are: 1. Side-Side-Side (SSS) criterion: If the three sides of one triangle are equal to the corresponding 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 equal to the corresponding 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 equal to the corresponding 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 equal to the corresponding two angles and the non-included side of another triangle, then the triangles are congruent. 5. Hypotenuse-Leg (HL) criterion: If the hypotenuse and one leg of a right-angled triangle are equal to the hypotenuse and one leg of another right-angled triangle, then the triangles are congruent.

Ans. To prove that two triangles are congruent using the Side-Side-Side (SSS) criterion, we need to show that all three sides of one triangle are equal to the corresponding three sides of the other triangle. Here are the steps to prove congruence using the SSS criterion: 1. Label the given triangles as Triangle ABC and Triangle PQR, where the corresponding vertices are A and P, B and Q, and C and R. 2. Measure the lengths of each side of Triangle ABC and Triangle PQR. 3. If the lengths of all three sides of Triangle ABC are equal to the lengths of the corresponding three sides of Triangle PQR, then we can conclude that the triangles are congruent by the SSS criterion.

Ans. The Angle-Side-Angle (ASA) criterion states that if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the triangles are congruent. Here's how to use the ASA criterion to prove congruence: 1. Label the given triangles as Triangle ABC and Triangle PQR, where the corresponding vertices are A and P, B and Q, and C and R. 2. Measure the angles of Triangle ABC and Triangle PQR using a protractor. 3. If two angles of Triangle ABC are equal to the corresponding two angles of Triangle PQR, and the included side between these angles in Triangle ABC is equal to the included side between the corresponding angles in Triangle PQR, then we can conclude that the triangles are congruent by the ASA criterion.

Ans. No, we cannot prove congruence of triangles using only the Angle-Angle-Side (AAS) criterion. The AAS criterion states that if two angles and a non-included side of one triangle are equal to the corresponding two angles and the non-included side of another triangle, then we can only conclude that the two triangles are similar, not congruent. To prove congruence, we need to have three corresponding parts (sides and angles) equal in both triangles, which is not possible with just the AAS criterion.

Ans. The Hypotenuse-Leg (HL) criterion states that if the hypotenuse and one leg of a right-angled triangle are equal to the hypotenuse and one leg of another right-angled triangle, then the triangles are congruent. To prove congruence using the HL criterion: 1. Label the given right-angled triangles as Triangle ABC and Triangle PQR, where the right angles are at vertices C and R, respectively. 2. Measure the lengths of the hypotenuse and one leg of Triangle ABC and Triangle PQR. 3. If the hypotenuse and one leg of Triangle ABC are equal to the hypotenuse and one leg of Triangle PQR, then we can conclude that the triangles are congruent by the HL criterion.