give:m is the midpoint of Ab,P is the midpoint of BC and N is the midpoint of AC :prove that AMPN is paralleiogram
This may help:
http://mathforlove.com/2012/02/midpoints-of-a-quadrilateral-form-a-parallelogram/
To prove that quadrilateral AMPN is a parallelogram, we need to show that opposite sides are parallel.
We are given that M is the midpoint of AB, P is the midpoint of BC, and N is the midpoint of AC.
To show that AM is parallel to PN, we need to show that AM and PN have the same slope.
1. Find the slope of AM:
- The coordinates of A and M are given.
- Use the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points.
- Substitute the values into the formula to find the slope of AM.
2. Find the slope of PN:
- The coordinates of P and N are given.
- Use the slope formula as in step 1 to find the slope of PN.
3. Compare the slopes:
- If the slopes of AM and PN are equal, then AM is parallel to PN.
Repeat steps 1-3 to show that MP is parallel to AN.
If both pairs of opposite sides, AM || PN and MP || AN, are parallel, then quadrilateral AMPN is a parallelogram.