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Standard IX
Mathematics
Why SSA and AAA Congruency Rule Is Not Valid
If three angl...
Question

If three angles of a triangle are equal to three angles of another triangle respectively, 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


The given statement is false. Even when two triangles have all angles same, they can still have sides of different lengths. However, the ratio of lengths of corresponding sides will be same. But in this case, they will be called 'similar' triangles, not congruent.

Congruent triangles are a special case of similar triangles.

For example, in the image below, both triangles are equilateral and have all angles equal but they are not congruent.


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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.
(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.
Q.

Question 102

State whether the statement is True or False.

If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent.

Q.

Question 99

State whether the statement is True or False.

If two legs of a right-angled triangle are equal to two legs of another right-angled triangle, then the right triangles are congruent.

Q.

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


Q. Consider the following statements:
i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.
ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.
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