Two triangles are said to be congruent triangles if all the sides and the interior angles of one triangle are equal to the corresponding sides and the corresponding interior angles of the other triangle. This implies that the corresponding sides and angles are of equal measure in both the triangles. In order to show that two triangles are congruent triangles, we can use the congruency properties and prove that the triangles are congruent.Congruency in between two triangles is denoted by the symbol ‘≡’.
Example 1: In triangle ABC, side AB = 6m side AC = 4m and angle BAC is 55º. In triangle XYZ, side XY = 6m, XZ = 4m and angle YXZ is 55º. Are ABC and XYZ congruent triangles?
Based on the above description, we can see the diagram here.
Given: AB= XY = 6m
AC= XZ = 4m
Angle BAC= angle YXZ = 55º
According to SAS (Side-included Angle-Side congruency property), corresponding 2 sides and an included
angle are equal in both the triangles and hence they are congruent triangles.
Example 2: Triangle PQR is an isosceles triangle with side PQ = side PR. If PS is drawn onto side QR and PS bisects the side QR, then are the triangles PQS and PRS congruent triangles?
Based on the above description, we can see the diagram here.
Given: PQ= PR
PS bisects side QR==> QS= SR
The side PS= side PS
According to SSS (Side-Side-Side congruency property), 3 sides of triangle PQS is congruent to 3 sides of
triangle PRS and hence triangle PQS is congruent to triangle PRS.
Example 1: In triangle ABC, side AB = 6m side AC = 4m and angle BAC is 55º. In triangle XYZ, side XY = 6m, XZ = 4m and angle YXZ is 55º. Are ABC and XYZ congruent triangles?
Based on the above description, we can see the diagram here.
Given: AB= XY = 6m
AC= XZ = 4m
Angle BAC= angle YXZ = 55º
According to SAS (Side-included Angle-Side congruency property), corresponding 2 sides and an included
angle are equal in both the triangles and hence they are congruent triangles.
Example 2: Triangle PQR is an isosceles triangle with side PQ = side PR. If PS is drawn onto side QR and PS bisects the side QR, then are the triangles PQS and PRS congruent triangles?
Based on the above description, we can see the diagram here.
Given: PQ= PR
PS bisects side QR==> QS= SR
The side PS= side PS
According to SSS (Side-Side-Side congruency property), 3 sides of triangle PQS is congruent to 3 sides of
triangle PRS and hence triangle PQS is congruent to triangle PRS.
