# Congruent Line-segments

In congruent line-segments we will learn how to recognize that two line-segments are congruent.

Two equal line-segments, lying in the same straight line and sharing a common vertex.

Here, two line-segments 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 line-segments.

 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 anti-clock 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”.Thus PQ ≅ R’S” i.e., RSTherefore, PQ ≅ RS.

Congruent Line-segments

Congruent Angles

Congruent Triangles

Conditions for the Congruence of Triangles

Side Side Side Congruence

Angle Side Angle Congruence

Angle Angle Side Congruence

Pythagorean Theorem

Converse of Pythagorean Theorem