Question

Which of the following is not a criterion for congruency of triangles?
(a) SAS
(b) ASA
(c) SSA
(d) SSS

Answer 1

Hint: To solve the above question we will first find out what congruency in the triangle is and then we will find out what the criteria for two triangles are to be congruent to each other. After doing this, we will look at options and check which option is not a criterion for congruency.

Complete step-by-step solution -
Before we solve the question given, we must know what congruency in the triangle is. Congruency is the property of the triangle by which we can tell that the two triangles have the same corresponding sides and corresponding angles. Thus, two triangles are said to be congruent if all three sides and three angles are equal. There are five rules of congruency.
(i) SSS rule or Side – Side – Side rule: This rule says that the two triangles will be congruent if their corresponding sides will be equal in length.
(ii) SAS rule or Side – Angle – Side rule: This rule says that the two triangles will be congruent if two sides and an included angle of one triangle are equal to those of the second triangle.
(iii) ASA rule or Angle – Side – Angle rule: This rule says that the two triangles will be congruent if two angles and the included side of one triangle are equal to those of the second triangle.
(iv) AAS rule or Angle – Angle – Side rule: This rule says that the two triangles will be congruent if two angles and a non-included side of one triangle are equal to those of the second triangle.
(v) RHS rule or Right Angle – Hypotenuse – Side rule: This rule says that the two right-angled triangles will be congruent if the hypotenuse and a side of one triangle are equal to that of another triangle.
Now, from the options, we can see that SSA is not amongst the above five rules, so it is not a criterion for congruency.
Hence, the option (c) is the right answer.

Note: We can also explain why option (c) is incorrect in the following way.
Let us consider two triangles: Triangle ABC and Triangle DEF. We assume that AB = DE and BC = EF and \[\angle B=\angle D.\]

From the above figures, we can see that the triangles are not congruent because the other angles and sides of one triangle will not be the same.