Question

ABCD is quite E,F,G and H are the midpoints of AB,BC,CD and DA respectively. prove that EFGH is a parallelogram.

Answer 1

This is the answer and if it is right please mark as brainliest

Answer 2

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$\underline\red{Given :-}$

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In ABCD Quadrilateral E, F, G, H are midpoints of

AB, BC, CD, DA respectively

$\underline\red{Required~to~prove :-}$

EFGH is parallelogram

$\underline\red{Proof :-}$

In Quadrilateral ABCD ,

AC is a diagonal.

In ∆ABC ; E, F are midpoints of AB, BC.

" The line segment joining the midpoints of two sides of a triangle is parallel to the third side "

$\huge{\fbox{\box{\red{EF~//~AC}}}}}$ → $\bf{(1)}$

In ∆ACD ; G, H are midpoints of DC, AD

By midpoint

$\huge{\fbox{\box{\red{GH~//~AC}}}}}$ → $\bf{(2)}$

from (1) & (2)

$\huge{\fbox{\box{\green{EF~//~GH}}}}}$ → $\bf{(i)}$

In Quadrilateral ABCD , BD I'd a diagonal

In ∆ABD ; E, H are midpoints of AB, AD

By midpoint

$\huge{\fbox{\box{\red{EH~//~BD}}}}}$ → $\bf{(3)}$

In ∆BCD ; F, G are midpoints of BC, CD

By midpoint

$\huge{\fbox{\box{\red{FG~//~BD}}}}}$ → $\bf{(4)}$

from (3) & (4)

$\huge\boxed{\fcolorbox{cyan}{Grey}{EH~//~FG}}$ $\simplies$ $\bf{(ii) }$

In Quadrilateral EFGH ,

EF // GH and EH // FG

$\therefore$ $\bf\yellow{EFGH~is~a~parallelogram}$

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$<marquee>Be... Brainly... ✔✔✔</marquee>$

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