Question

given: ∠lno ≅ ∠lnm
∠oln ≅ ∠mln
prove: △lno ≅ △lnm
diagram of triangles with vertices l, n, o, m
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 dropdown lnm.
options (partial): vertical angles, asa, aaa, the reflexive property

Explanation:

Step1: Identify the congruent angle (first blank)

Given \(\angle LNO \cong \angle LNM\), so the first blank is filled with \(\angle LNM\).

Step2: Identify the congruent angle (second blank)

Given \(\angle OLN \cong \angle MLN\), so the second blank is filled with \(\angle MLN\).

Step3: Identify the property for side \(LN\)

Side \(LN\) is congruent to itself, which is due to the reflexive property. So the third blank is "the reflexive property".

Step4: Identify the triangle congruence criterion

We have two angles and the included side ( \(LN\) ) congruent, so the criterion is ASA (Angle - Side - Angle). So the fourth blank is "ASA".

Answer:

First blank: \(\angle LNM\); Second blank: \(\angle MLN\); Third blank: the reflexive property; Fourth blank: ASA