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Difference between Congruency and Similarity

If three angl...

Question

If three angles of a triangle are equal to the corresponding three angles of another triangle then the two triangles are congruent.

A

True

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B

False

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Solution

The correct option is B False
If three angles of a triangle are respectively equal to three angles of another triangle then the two triangles are not necessarily congruent because we have no idea about the sides of the two triangles. If the sides of the two triangles are completely different in lengths then the two triangles are not congruent.
However, the ratio of lengths of corresponding sides will be same. But in this case, they will be called 'similar' triangles, not congruent.
Hence, the above statement is false.

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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.
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(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
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