Question

In triangles $ABCandPQR$, three equality relations between some parts are as follows:

$\mathrm{AB}=\mathrm{QP},\angle \mathrm{B}=\angle \mathrm{P}\mathrm{and}\mathrm{BC}=\mathrm{PR}$

State which of the congruence conditions applies:

• A. SAS
• B. SSS
• C. ASA
• D. RHS

Answer 1

The correct option is A

SAS

Explanation for the correct option:

Option (A) : SAS

It is given that $\mathrm{AB}=\mathrm{QP},\angle \mathrm{B}=\angle \mathrm{P}\mathrm{and}\mathrm{BC}=\mathrm{PR}$

SAS Congruence: two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other triangle.

Therefore, triangles $ABCandQPR$ are congruent by SAS Congruence criterion.

Explanation for the incorrect option:

Option (B): SSS

In SSS Congruence three sides of the two angles are equal but the given data does not satisfy the criterion.

Therefore, it is not the correct criterion.

Option (C) : ASA

In this ASA congruence two angles and one side of two triangles are equal but the given data does not satisfy the condition.

Therefore, it is not the correct criterion.

Option (D): RHS

In this the hypotenuse and one side of two triangles are equal but the given data does not satisfy the condition.

Therefore, it is not the correct criterion.

Hence, option (A) is the correct option.