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ASA Criteria for Congruency

Are two trian...

Question

Are two triangles congruent if two sides and an angle of one triangle are respectively equal to two sides and an angle of the other? If not then under what conditions will they be congruent?

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Solution

No, two triangles are not congruent if their two corresponding sides and one angle are equal. They will be congruent only if the said angle is the included angle between the sides.

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Q. Which of the following statements is CORRECT?
Statement-1 : Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.
Statement-2 : Two triangles are congruent if two sides and the included angle of the one must be equal to the corresponding two sides and included angle of the other.

Q. Assertion :Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other. Reason: Two triangles are congruent if two sides and the included angle of the one must be equal to the corresponding two sides and included angle of the other.
Which of the following options hold?

Q. If the two sides and the ____ angle of one triangle are respectively equal to two sides and the included angle of the other triangle, then the triangles are congruent.

Q. If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent by ____ congruence condition.

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.

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