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Sagot :
Answer:
The answer is "[tex]\bold{\Delta LNO \cong \Delta LMN \ if\ \angle LNO = \angle LNM}[/tex]"
Step-by-step explanation:
Two angles will be congruent to each other in order to show ASA congruence between all the triangles. Its angle [tex]\angle LNO \cong \angle LNM[/tex] is a common angle in both triangles As a result, we'll use the ASA congruence law to show that perhaps the triangles are congruent.
[tex]In\ \Delta LON \ and \ \Delta LMN \\\\ Side\ \ ON \cong Side\ \ MN \\\\\angle LNO \cong \angle LNM ( \because common ) \\\\ \angle LON \cong \angle LMN (\because Given ) \\\\\to \Delta LON \cong \Delta LMN \text{( through the ASA congruence theorem)}\\[/tex]
The additional information required to prove that the triangles are congruent using the ASA congruence theorem is; ∠LNO ≅ ∠LNM
- We are given that;
△LON and △LMN share a common side LN.
This means that for both triangles LN = LN by reflexive property as LN is congruent to itself.
- Secondly, we are told that;
∠OLN and ∠NLM are congruent.
We can see that L is an included angle of the congruent side LN.
- Now, ASA congruency means Angle - Side - Angle. That means two congruent angles and the included side.
- Thus, we need one more angle of the included side LN.
We already have for L, and so the remaining angles that will make△LON and △LMN congruent are;∠LNO and ∠LNM.
Read more on ASA Congruence at; https://brainly.com/question/3168048
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