Question

M and N are the midpoints of sidesPQ and PR of triangle PQR. Ol is parallel to RN. Prove that LNRQ is a parallelogram ​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

Before we attempt,

Mid Point theorem:-

If the mid points of a triangle are joined, then it will be parallel to the third side of the triangle.

• M and N are the midpoints of the Triangle PQR.
• So according to the mid point theorem:-
• MN will be parallel to QR.

• We are given that LQ is parallel to NR.

Also, we need to keep in mind that:-

• corresponding sides of parallelogram are parallel
• They are also equal to each other.

So, LQRN is a parallelogram.

Hence proved.

Answer 2

Given:

• M is midpoint of PQ
• N is midpoint of PR
• QL is parralel to NR.

━━━━━━━━━━━━━━━━━━━

Need to prove :

• LNRQ is a parallelogram.

━━━━━━━━━━━━━━━━━━

Solution:

According to Mid point theorem:

If the midpoints of two sides of a triangle is joined then the line joining the two sides will be parallel to the third side and will be half of it.

Consider the triangle PQR,

• MN is the line joining midpoint of PQ and PR
• Thus MN//QR (by mid point theorem)

━━━━━━━━━━━━━━━━━━

We know if the opposite sides of a quadrilateral are parallel to each other then the quadrilateral is called a parallelogram.

Thus as MN// QR and given QL//NR, we can say that LNRQ is a parallelogram.