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Introduction to Congruence

Two rectangle...

Question

Two rectangles are congruent, if they have same and .

A

Length

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B

Breadth

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Solution

Congruent:-Congruence is a term used to describe the relationship between two congruent figures. In terms of shape and size, the word ‘congruent’ implies equal in every aspect or figure.
So, two rectangles can only be congruent if their length and breadth is same.

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Similar questions

Q. Fill in the blanks:

(i) Two lines segments are congruent if they have ...... .
(ii) Two angles are congruent if they have ...... .
(iii) Two squares are congruent if they have ...... .
(iv) Two circles are congruent if they have ...... .
(v) Two rectangles are congruent if they have ...... .
(vi) Two triangles are congruent if they have ...... .

Q. In two triangles ABC and ADC, if AB = AD and BC = CD. Are they congruent?

Q. Which of the following statements are true and which are false;
(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two rectangles have equal area, they are congruent.
(iv) If two triangles are equal in area, they are congruent.

Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

Statement 1: If two figures A and B are congruent, then they must have equal area.

Statement 2: If two figures A and B have equal area, then they must be congruent.

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