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Triangles L O N and L M N share common side L N. Angles O L N and N L M are congruent. What additional information would be needed to prove that the triangles are congruent using the ASA congruence theorem? ON ≅ MN ∠LON ≅ ∠LMN LN ≅ NM ∠LNO ≅ ∠LNM

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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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