Question

It is given that $LM = ON$ and $NL = MO$.
A) State the three pairs of equal parts in the triangles $NOM$ and $MLN$
B) Is $\vartriangle NOM \cong \vartriangle MLN$. Give reason?

Answer 1

Hint: In this question, they give relations of two triangles. We have to find the required result. In order to solve this question we have to prove that the sides of the triangle are equal in length. Use the congruence properties to prove that the triangles are congruent.

Complete step-by-step answer:
From given diagram:

It is stated in the question that $LM = ON$ and $NL = MO$.
A) State the three pairs of equal parts in the triangles $NOM$ and $MLN$
In $\vartriangle MLN$ and $\vartriangle NOM$ we get-
$NM = MN$ as it is the same line
$NL = MO$ since it is given in the question
$LM = ON$ already stated in the question
Hence it is proved that the three pairs of equal parts in the triangles $NOM$ and $MLN$.
B) Is $\vartriangle NOM \cong \vartriangle MLN$. Give reason?
When all the sides of the two triangles are equal, then it can be said that the two triangles are congruent.
Since in triangle $\vartriangle MLN$ and $\vartriangle NOM$ we get-
$NM = MN$ since it is the same line
$NL = MO$ and $LM = ON$ as already given in the question.
Hence it can be said that $\vartriangle NOM \cong \vartriangle MLN$ since all the sides of both the triangles are equal.

Note: When all the three sides and three angles of the two triangles are equal then the two triangles can be said to be congruent.
The main conditions for congruency are given below:
If all the sides of one triangle are equal to all the three sides of the other triangle, then the two triangles are said to be congruent.
If two sides of a triangle and the angle present between them is equal to the other two sides and angle present between them of another triangle, then the two triangles are regarded as congruent.
If any two angles and a side of a triangle is equal to the two angles and one side of the other triangle, then the two triangles are said to be congruent.