Question

Which pair of triangles are congruent by $ASA$ ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The explanation for the correct option:

Correct option $\left(D\right)$:

• ASA Congruence Rule ( Angle – Side – Angle ) State that,
• Two triangles are said to be congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• From the given options, It is observed that In option (d), two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Hence, the option $\left(D\right)$ is correct.

The explanation for the incorrect options.

Option $\left(A\right)$:

The given triangles of the option $\left(A\right)$ are not congruent by any congruency rule.

Thus, option $A$ is incorrect.

Options $B$ and $C$:

• The SAS rule states that. If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
• It is observed that the given triangles of the option $\left(B\right)$ and $\left(C\right)$ are congruent by $\mathrm{side}-\mathrm{angle}-\mathrm{side}\left(\mathrm{SAS}\right)$ congruency rule.

Thus, options B and C are incorrect.

Hence, the option $\left(D\right)$ is correct.