It is given that angle LNO is congruent to angle LNM and angle OLN is congruent to angle MLN. We know that side LN is congruent to side LN because of the Reflexive property of congruence. Therefore, because of ASA congruence postulate, we can state that triangle LNO is congruent to triangle LNM. This is obtained by understanding the ASA rule.
What is ASA congruence postulate?
- The two angles and the included side of one triangle is equal to two angles and the included side of another triangle.
- Such triangles are called congruent according to ASA congruence postulate.
Find the blanks in the question:
- In the question, it is clear that angle LNO = angle ONL from the given figure.
- Also, angle OLN = angle MLN from the given figure.
- Since common side LN and LN are equal, the property is called Reflexive property of congruence.
- Therefore from the figure we can say that, the two angles and the included side of one triangle is equal to two angles and the included side of another triangle, which is the ASA congruence postulate.
Hence the blanks can be filled with angle LNM, angle MLN, Reflexive property of congruence and ASA congruence postulate.
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