Question

given: ∠lno ≅ ∠lnm
∠oln ≅ ∠mln
prove: △lno ≅ △lnm
it is given that angle lno is congruent to angle
and angle oln is congruent to angle
we know that side ln is congruent to side ln because of the
therefore, because of
, we can state that triangle lno is congruent to triangle lnm.

Explanation:

Step1: Identify given congruent angles

We are given $\angle LNO\cong\angle LNM$ and $\angle OLN\cong\angle MLN$.

Step2: Recognize reflexive property

Side $LN$ is congruent to itself by the reflexive property of congruence.

Step3: Apply congruence criterion

Since we have two pairs of congruent angles and the included - side congruent, by the Angle - Side - Angle (ASA) congruence criterion, $\triangle LNO\cong\triangle LNM$.

Answer:

It is given that angle $LNO$ is congruent to angle $LNM$ and angle $OLN$ is congruent to angle $MLN$. We know that side $LN$ is congruent to side $LN$ because of the reflexive property. Therefore, because of the Angle - Side - Angle (ASA) congruence criterion, we can state that triangle $LNO$ is congruent to triangle $LNM$.