And in congruent shape, two figures can be placed over each other. In congruent figures, the shape and size should remain equal when we flip, turn or even rotate the shapes. We understand that identical shapes and sizes are called congruent in geometry. Therefore, both the circles are similar to each other, but they are not congruent to each other. In the above diagram, the length of the radius OL is equal to 2 cm, whereas OM is equal to 1 cm.įor two circles to be congruent to each other, the length of the radius of both the circles should be equal to each other. Mention the corresponding sides and angles that will be equal.Īs per CPCT, all the three corresponding sides and angles of congruent triangles ∆MNO and ∆XYZ will be equal to each other.Įxample 3: Are the below figures similar or congruent to each other? Therefore, ∠ ABC is not congruent to ∠ XYZ.Įxample 2: Two triangles MNO and XYZ are congruent. Measure of ∠ ABC is not equal to measure of ∠ XYZ. The measure of ∠ ABC = 40° and ∠ XYZ = 60°. Solved ExamplesĮxample 1: Are the two angles ∠ ABC and ∠ XYZ congruent to each other? However, they are not congruent to each other. Hence, MNO and XYZ are similar to each other. The length of the corresponding sides are not equal to each other. Only the angles are equal to each other, which are ∠ M = ∠ X, ∠ N = ∠ Y and ∠ O = ∠ Z.

Whereas, with respect to Similar Figures. Therefore, ABC ≅ DEF, as both the corresponding angles and the lengths of the corresponding side are equal to each other. However, the lengths of the corresponding sides are not equal to each other.Īs per the above diagram, Congruent Figures are represented by ABC and DEF, whereas Similar Figures are represented by MNO and XYZ This is because the corresponding angles are equal. In two similar figures, the shapes look the same. In two congruent figures, both the corresponding angles and the lengths of the corresponding sides are equal to each other. The significant difference between congruent figures and similar figures is that: Congruent Figures Whenever two or more triangles are congruent, their corresponding sides and angles are also congruent by the rule of Corresponding Parts of Congruent Triangles (CPCT), Difference between Congruent Figures and Similar Figures Congruent TrianglesĪ triangle has 3 sides and 3 angles,so for triangles to be congruent all 3 sides and angles should be congruent. To conclude, Circle A is congruent to Circle B, and it can be written as Circle A ≅ Circle B. It also means that both the circles can be easily placed over each other. The shape of both the circles is the same and the size is also the same as the length of radii OR and OP is equal to 2 cm each.Īs per the condition of congruency, if the radius of two circles are equal in length, then both the circles are congruent to each other. In the above diagram, the radius of Circle A is represented by radius OR, whereas the radius of Circle B is represented by OP. If we superimpose or overlap ∠ ABC on ∠ PQR, we will find that both the angles are congruent to each other.Īs per the rule, two angles are congruent if the measures of both the angles are equal to each other. In the above diagram, ∠ ABC = 40 °, whereas ∠ PQR = 40 °. Therefore, it will be represented as line segment AB ≅ line segment PQ. Hence, the line segments AB and PQ are congruent with each other. So, if two or more lines are equal in length, they are said to be congruent to each other. Hence, the length of both line segments are equal to each other. The length of line segment AB is equal to 5 cm and PQ is also equal to 5 cm. Since both AB and PQ are line segments they are of the same shape. Since congruence implies equal shape and size, the line segments will be congruent if their shape and size is the same.

If two objects A and B are congruent to each other, we will write it as: A ≅ B Congruent Line Segments Hence, congruence is represented by the symbol as ‘ ≅ ’ There is a symbol of tilde “ ” which represents similarity in shape and “=” represents equality in size. Since congruence in objects implies equal shape and size the symbol of congruence is made of two symbols, one above the other. Two lego bricks which represent equal shape and size Symbol of CongruenceĬongruence is represented by the symbol- ‘ ≅ ’ Two candy ice creams which represent equal shape and size Two butterflies which have equal shape and size This shape and size should remain equal, even when we flip, turn, or rotate the shapes. The term “congruent” means exactly equal shape and size. If you place one slice of bread over the other, you will find that both the slices are of equal shape and size. If two figures can be placed precisely over each other, they are said to be ‘congruent’ figures.

Congruent shapes