Question

proving triangle congruence
given: ∠lno ≅ ∠lnm
∠oln ≅ ∠mln
prove: △lno ≅ △lnm
it is given that angle lno is congruent to angle dropdown and angle oln is congruent to angle dropdown. we know that side ln is congruent to side ln because of the dropdown. therefore, because of dropdown, we can state that triangle lno is congruent to triangle lnm.
image of triangle with vertices l, o, n and l, m, n, sharing side ln, with marked congruent angles at n and at l

Explanation:

Step1: Identify Congruent Angles

From the given, $\angle LNO \cong \angle LNM$ (so first blank: $\angle LNM$) and $\angle OLN \cong \angle MLN$ (second blank: $\angle MLN$).

Step2: Identify Common Side

Side $LN$ is common to both $\triangle LNO$ and $\triangle LNM$. By the Reflexive Property of Congruence, a side is congruent to itself (third blank: Reflexive Property).

Step3: Determine Congruence Criterion

We have two angles and the included side (ASA: Angle - Side - Angle) congruent. So the congruence criterion is ASA (fourth blank: ASA).

Answer:

First blank: $\angle LNM$; Second blank: $\angle MLN$; Third blank: Reflexive Property; Fourth blank: ASA