Question

In triangles$\mathrm{ABC}\mathrm{and}\mathrm{PQR},\mathrm{if}\angle \mathrm{A}=\angle \mathrm{R},\angle \mathrm{B}=\angle \mathrm{P}\mathrm{and}\mathrm{AB}=\mathrm{RP},$then which one of the following congruence condition applies:

• A. SAS
• B. SSS
• C. ASA
• D. RHS

Answer 1

The correct option is C

ASA

Explanation for the correct option:

Option (C) : ASA

It is given that $\angle \mathrm{A}=\angle \mathrm{R},\angle \mathrm{B}=\angle \mathrm{P}\mathrm{and}\mathrm{AB}=\mathrm{RP}$

ASA Congruence: Two triangles are congruent, if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.

As we know that two angles and one side of two triangles are equal,

Therefore $△\mathrm{ABC}\cong △\mathrm{PQR}$ by ASA congruence criterion.

Explanation for the incorrect option:

Option (A) : SAS

The given data does not fit this criterion as in this two sides and one angle of two triangles should be equal.

Therefore, SAS congruence is not the correct criterion.

Option (B) : SSS

The given data does not fit the condition required as in SSS congruence all the three sides of two triangles are equal.

Therefore, SSS congruence is not the correct criterion.

Option (D) : RHS

In this criterion, the hypotenuse and one side of two triangles are equal which is not data given.

Therefore, RHS congruence is not the correct criterion.

Hence, option (C) is the correct option.