Question

given: \\( \angle lno \cong \angle lnm \\) \\( \angle oln \cong \angle mln \\) prove: \\( \triangle uno \cong \triangle unm \\) 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:

• For the first blank: Given \(\angle LNO\cong\angle LNM\), so the first blank is \(\angle LNM\).
• For the second blank: Given \(\angle OLN\cong\angle MLN\), so the second blank is \(\angle MLN\).
• For the third blank: A side is congruent to itself by the reflexive property of congruence. So, side \(LN\) is congruent to side \(LN\) because of the reflexive property.
• For the fourth blank: We have two angles and the included side ( \(ASA\) - Angle - Side - Angle) congruent. Since \(\angle LNO\cong\angle LNM\), \(LN = LN\) (reflexive property), and \(\angle OLN\cong\angle MLN\), by the \(ASA\) (Angle - Side - Angle) congruence criterion, \(\triangle LNO\cong\triangle LNM\).

Answer:

First blank: \(\angle LNM\), Second blank: \(\angle MLN\), Third blank: reflexive property, Fourth blank: \(ASA\) (Angle - Side - Angle)