Question

Out of the following which is not the test for congruence of triangles
A.SAS
B.SSS
C.AAA
D.ASA

Answer 1

Hint: In order to approach the correct option for a test for congruence, we must know what congruence is, and what are the rules being followed for two triangles to be congruent. Check out the options that are not present in the rules.

Complete step by step solution:
Before solving the question, we must know what congruency in the triangle is. Congruence is the property of triangles by which we can compare that the two triangles have the same corresponding sides and corresponding angles. The two triangles are said to be congruent if all the three sides and the three angles are equal.
We know that there are five rules of congruency, which are as follows:

I.SSS rule (Side- Side-Side): According to this property if all the corresponding sides of two triangles are equal, the triangles are congruent.

II.SAS rule (Side-Angle-Side): According to this rule, the corresponding sides and the included angle for the two triangles must be equal in order to be congruent.

III.ASA rule (Angle-Side-angle): According to this rule, two angles and the included side for the two triangles, must be equal. Then the two triangles would be congruent.

IV.AAS rule (Angle-Angle-Side): According to this rule, two angles and one non-included side for the two triangles, must be equal. Then the two triangles would be congruent.
RHS rule (Right Angle-Hypotenuse-Side rule): This rule says that two-right angled triangles will be congruent if the hypotenuse and one side for two triangles are equal.
These are rules or tests for congruency of a triangle, apart from these five any other rule would not be followed.
So, from the Options, we can see that Option C, i.e. AAA (Angle-Angle-Angle) is not included, therefore it cannot be used for the test of congruence.
Hence, Option C is correct.
So, the correct answer is “Option C”.

Note: Congruence can be checked for any two 2-dimensional objects, like two-line segments, and two angles, two triangles, etc.
Two triangles are congruent, if they are of the same shape and size, if any one of two is bent or stretched or twisted, they are no more congruent.
The sign of congruence is $ \cong $ .