In congruent linesegments we will learn how to recognize that two linesegments are congruent.
Two equal linesegments, lying in the same straight line and sharing a common vertex.
Here, two linesegments XY and YZ lying in the same straight line are equal. This is to be verified that they are congruent.
ab is perpendicular drawn at Y on XZ. With respect to ab, the image of ZY is YZ’. XY = YZ Hence, Z’ lies on X
Therefore, XY ≅ YZ 
Taking Y as the centre of rotation and rotating YZ through an angle 180° in anticlockwise direction, the image YZ’ is obtained, where Z’ lies on X Therefore, XY ≅ YZ 
Two line segments lie on the same plane but at different positions.
PQ and RS are two equal line segments on the same plane but on different positions. It is verified that they are congruent linesegments.
Perpendicular bisector XY of PR is drawn. Taking XY as the axis of reflection, the image of RS and PS’. Now taking P as the centre of rotation and rotating PS’ through such an angle (in anticlock wise direction), so that PS’ coincides with PQ. Since PS’ that is RS = PQ. Hence S’ lies on Q and its new name is D”. 
Conditions for the Congruence of Triangles
Right Angle Hypotenuse Side congruence
Converse of Pythagorean Theorem
7th Grade Math Problems
8th Grade Math Practice
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