ABCD is a quadrilateral, P Q R and S divide AB, CB, CD and AD in ratio 1:3 respectively. Prove that a//m. (Please hurry up, I will mark you as Brainliest) ​

Two lines are parallel if they are equidistant from one another. The following proves

means that:

To prove that is to prove that side length SR and side length PQ are parallel because:

--------- See attachment for quadrilateral

Considering , we have:

Divide both sides by PA

Similarly:

Divide both sides by QC

So, we have:

Express as ratios

means point P divided side length BA into 3:1

means point Q divided side length BC into 3:1

Thales Theorem states that: A line that divides any two sides of a triangle in the same ratio is parallel to the third side.

The third side of is .

This means that: is parallel to

Since is parallel to , then is parallel to

i.e.

Recall that:

Hence:

has been proved.

Read more about proof of parallel sides at:

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2) 19

3) 1134

Step-by-step explanation: