Question

Which of the following is sufficient for two triangles denoted by $\Delta 1$ and $\Delta 2$ to be congruent ?

• A. Any two sides of $\Delta 1$ should be equal to any two sides of $\Delta 2$
• B. All angles of $\Delta 1$ should be equal to all angles of $\Delta 2$
• C. Any two sides of $\Delta 1$ and one angle should be equal to any two sides and one angle of $\Delta 2$
• D. Any two sides of $\Delta 1$ and the included angle should be equal to any two sides and the included angle of $\Delta 2$

Answer 1

The correct option is D

Any two sides of $\Delta 1$ and the included angle should be equal to any two sides and the included angle of $\Delta 2$

Two triangles can't be congruent if any two sides and one angle of one are equal to any two sides and one angle of the other.
They will be congruent when the angle is included between the equal pair of sides. This is the SAS condition of congruency of triangles.

The SAS congruence rule states:
Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.