It is given that angle \( \angle LNO \) is congruent to angle \( \angle NLO \) and angle \( \angle OLN \) is congruent to angle \( \angle NML \). We know that side \( \overline{LN} \) is congruent to side \( \overline{LN} \) because of the Reflexive Property. Therefore, because of the Angle-Side-Angle (ASA) Congruence Postulate, we can state that triangle \( \triangle LNO \) is congruent to triangle \( \triangle LNM \).

Question

20-10-2023
Mathematics

High School

Thank you for visiting It is given that angle angle LNO is congruent to angle angle NLO and angle angle OLN is congruent to angle angle NML We know. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

It is given that angle \( \angle LNO \) is congruent to angle \( \angle NLO \) and angle \( \angle OLN \) is congruent to angle \( \angle NML \). We know that side \( \overline{LN} \) is congruent to side \( \overline{LN} \) because of the Reflexive Property. Therefore, because of the Angle-Side-Angle (ASA) Congruence Postulate, we can state that triangle \( \triangle LNO \) is congruent to triangle \( \triangle LNM \).

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rachanavt02 rachanavt02 · Answer 1 · 2023-09-02T06:25:48-04:00

The triangle LNO is congruent to triangle LNM by the SAS Congruence Theorem.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

It seems that there is some missing information in the question as the congruence of angle LNO and angle MNO is not specified. However, assuming that angle LNO is congruent to angle MNO, and angle OLN is congruent to angle OMN, we can use the following congruence theorem to prove that triangle LNO is congruent to triangle LNM:

By the Side-Angle-Side (SAS) Congruence Theorem, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case, we know that side LN is congruent to side LN (by the reflexive property), and angle LNO is congruent to angle MNO, and angle OLN is congruent to angle OMN. Therefore, we can conclude that triangle LNO is congruent to triangle LNM by the SAS Congruence Theorem.

To learn more about the congruent;

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