SOLUTION: Please help! Problem: "Prove that the figure formed by connecting the midpoints of the sides of any quadrilateral is a parallelogram. Hint: a line segment connecting the midpoints

Question 62348: Please help! Problem: "Prove that the figure formed by connecting the midpoints of the sides of any quadrilateral is a parallelogram. Hint: a line segment connecting the midpoints of 2 sides of a triangle is parallel to the 3rd side."
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Please help! Problem: "Prove that the figure formed by connecting the midpoints of the sides of any quadrilateral is a parallelogram. Hint: a line segment connecting the midpoints of 2 sides of a triangle is parallel to the 3rd side.
LET ABCD BE THE QUADRILATERAL AND E,F,G,H BE THE MIDPOINTS OF AB,BC,CD,DA.
JOIN EFGH.JOIN THE DIAGONAL AC.
IN TRIANGLE ABC,
E IS MID POINT OF AB AND F IS THE MID POINT OF BC.....GIVEN
HENCE EF||AC AND
EF=AC/2......AS PER THEOREM.
SIMILARLY IN TRIANGLE ADC ,
G IS MIDPOINT OF CD AND H IS MIDPOINT OF AD.
HENCE GH||AC AND
GH = AC/2..AS PER THEOREM.
HENCE EF=GH.
IN THE FIGURE EFGH,EF||GH AND EF=GH.
HENCE EFGH IS A PARALLELOGRAM
RELATED QUESTIONS
Prove that the quadrilateral formed by connecting the midpoints of the sides of... (answered by ikleyn,Edwin McCravy)

Given: Quadrilateral PQRS P= (-10,7), Q=(4,3), R=(-2,-5), S=(-16,1) a.Prove taht the... (answered by jsmallt9)

The quadrilateral formed by joining the midpoints of the sides of a parallelogram... (answered by srinivas.g,Edwin McCravy,AnlytcPhil)

Prove that the line joining the midpoints of consecutive sides of a quadrilateral is a... (answered by ikleyn)

Use the coordinate plane, the figure below, coordinate proof strategies, and the lengths... (answered by math1745)

if a triangle has sides of 6,8 and 12, what is the perimeter of the triangle formed by... (answered by oscargut)

My daughter did not get this right on a test: Test question: With a straightedge draw a (answered by scott8148)

Prove that the triangle formed by joining the midpoints of the sides of an isosceles... (answered by mananth)