Question

In $\Delta JKL$ and $\Delta MNO$, $JL\cong ON$ and $KL\cong OM$, then the condition which will make both triangles congruent is:

• A. $\angle L\cong \angle O$
• B. $\angle K\cong \angle M$
• C. $\angle J\cong M$
• D. $\angle J\cong \angle N$

Answer 1

The correct option is A $\angle L\cong \angle O$

Two triangles can be congruent by the SAS test, since here we are equating two sides and one angle.

For the SAS test of congruency, the condition is that the angle must be included between the two sides to ensure correctness of the test.

Similarly, here the two included angles must be congruent for the triangles to be congruent.

They are $\angle L\cong \angle O$ since they are the included angles of sides $JL-KL$ and $ON-OM$ respectively.