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.

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”. |

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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