Choose the correct statements.

Two line segments with same length are always congruent.

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All concentric circles are congruent.

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All the angles of any square are congruent.

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All right angled triangles are congruent if they have hypotenuse of same length.

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Solution

The correct options are
A Two line segments with same length are always congruent.
C All the angles of any square are congruent.
Line segments are congruent if they have the same length.

Concentric circles are circles having the same center, but they may or may not have the same radii. So, they are not always congruent.

All angles in a square are equal to $90^{\circ}$ , so they are always congruent in any square.

A right angled triangle is congruent to another if they have equal lengths of the hypotenuse and a side.

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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. 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.

Consider the two statements:

Statement 1: If two line segments have the same length, then they are congruent.
Statement 2: If two line segments are congruent, then they have the same length.

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

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.

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