Question

Show that the figure formed by joining the midpoints of rhombus successively is a rectangle.

Answer 1

This is the answer Of your question

Answer 2

$<font color=red>$

║▌│█║▌│ █║▌│█│║▌║

$\huge{\fbox{\fbx{\bigstar{\mathbb{\pink{ÂnsWêr}}}}}}$

${\overbrace{\underbrace{\purple{EcstasyQueen}}}}$

$\underline\red{Given :-}$

$<font color=blue>$

ABLE is a Rhombus

P, Q, R, S are midpoints of the sides .

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

$<font color=blue>$

PQRS is Rectangle .

$\underline\red{Proof :-}$

$<font color=blue>$

We know that

"The Quadrilateral formed by joining of the midpoints of any Quadrilateral is a Parallelogram"

$\therefore\orange$ PQRS is a parallelogram

In ABCD Rhombus , S, Q are midpoints of opposite sides ĀD , BC .

so , $\huge{\fbox{\box{\bf{\red{SQ~=~AB~=~CD}}}}}$ $\simplies{1}$

P , R are midpoints of opposite sides AB , CD

$\huge{\fbox{\box{\bf{\red{PR~=~BC~=~AD}}}}}$$\simplies{2}$

But , In Rhombus ABCD all the sides are equal

$\huge{\fbox{\box{\bf{\red{AB~=~BC~=~CD~=~DA}}}}}$ $\simplies{3}$

from 1 , 2 & 3

$\huge{\fbox{\box{\bf{\green{SQ~=~PR}}}}}$

In parallelogram PQRS , the diagonals SQ , PR are equal

$\therefore\orange$ $\bf\green{PQRS~is~a~rectangle}$

$<font color=orange>$

$<marquee>EcstasyQueen</marquee>$

$<font color=red>$

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

║▌│█║▌│ █║▌│█│║▌║