Question

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

Answer 1

Answer is ∠LNO ≅ ∠LNM

Answer 2

ΔLNO ≅ ΔLMN iff ∠LNO = ∠LNM

Explanation:

Lets get started using the statement that...

In ΔLON and ΔLMN

Side ON ≅ Side MN

Side LN ≅ Side NM

∠LON ≅ ∠LMN

To Prove: ∠LON ≅ ∠LMN by ASA congruence theorem.

Solution: In order to prove ASA congruence between the triangles we need two angles to be congruent to each other. When we look at the figure, we see that ∠LNO ≅ ∠LNM is a common angle in both the triangles.

Hence, using this we will prove that the triangles are congruent by ASA congruence rule.

In ΔLON and ΔLMN

Side ON ≅ Side MN

∠LNO ≅ ∠LNM ( ∵ common )

∠LON ≅ ∠LMN (∵ Given )

⇒ ΔLON ≅ ΔLMN ( By ASA congruence theorem).