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Which of the following is a FALSE statement? 

A) Two line segments of same length are congruent. 

B) Two circles of same radii are congruent. 

C) Two angles of same measure are congruent. 

D) Two triangles of same area are congruent

2 Answers

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Correct option is (D) Two triangles of same area are congruent

(i) Two line segments of same length are congruent.

(ii) Two circles of same radii are congruent.

(iii) Two angles of same measures are congruent.

(iv) Two triangles of same area are not congruent.

Triangles \(\triangle ABC\;\&\;\triangle ABD\) are on same base AB and between same parallels AB & CD.

\(\therefore\) Area \((\triangle ABC)\) = Area \((\triangle ABD)\)

But \(\triangle ABC\cong\triangle ABD\)

as \(\angle ABD=90^\circ\) but no angle in \(\triangle ABC\) is a right angle.

Hence, two triangles of same area need not be congruent.

+1 vote
by (38.9k points)

D) Two triangles of same area are congruent

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