Congruent Shapes

In congruent shapes or congruent figures we will learn how to recognize that when two shapes or figures are congruent.  

The two figures which are same shape and same size are called congruent figures and the relation of two figures being congruent is called congruence.

The symbol to denote congruence is .  

Two line segments are congruent if both have the same length.

Congruent Line Segments

Congruent line segments

Two circles are congruent if both of them have the same radii.

Congruent Circles

Congruent circles


Two triangles are congruent if both of them have the same length of sides.

Congruent Triangles

Congruent triangles


Two rectangles are congruent if both of them have the opposite sides are equal.

Congruent Rectangle

Congruent rectangle

Two squares are congruent if both of them have the same edges.

Congruent Squares

Congruent squares


Thus, the method of comparing two figures is known as the method of superposition.

Congruent or Similar

Congruent shapes:

Two geometrical shapes which are identical in shape and size are said to be congruent. We use the symbol ‘’ to denote congruence.

For example:

(i) Two circle of same radii.

(ii) Two line segments of same length.

Similar shapes:

Geometrical shape which have same shape but different size are called similar shape or figure. We use the symbol ‘~’ to denote similarly.

For example:

(i) Two circle of different radii.

(ii) Two line segments of different measure.

Note: Two congruent figures are always similar but two similar figures may not be congruent.

Congruent Shapes

Congruent Line-segments

Congruent Angles

Congruent Triangles

Conditions for the Congruence of Triangles

Side Side Side Congruence

Side Angle Side Congruence

Angle Side Angle Congruence

Angle Angle Side Congruence

Right Angle Hypotenuse Side congruence

Pythagorean Theorem

Proof of Pythagorean Theorem

Converse of Pythagorean Theorem

7th Grade Math Problems

8th Grade Math Practice

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