Question

prove that the figure obtained by joining the midpoints of the adjacent sides of a quadrilateral is parallelogram

Answer 1

To Prove :- the figure obtained by joining the midpoints of the adjacent sides of a quadrilateral is parallelogram ?

Solution :-

from image , in ΔDAC we have,

• R = mid point of DC .
• S = mid point of DA.

So, by mid point theorem,

→ SR || AC

→ SR = (1/2)AC . ----------- Eqn.(1)

Similarly, in ΔBAC we have,

• P = mid point of AB .
• Q = mid point of BC.

So, by mid point theorem,

→ PQ || AC

→ PQ = (1/2)AC. ---------- Eqn.(2)

from Eqn.(1) and (2), we get,

→ SR = (1/2)AC = PQ

→ SR = PQ

and,

→ SR || AC || PQ

→ SR || PQ .

Opposite sides of PQRS are Parallel and equal..

Therefore, we can conclude that, PQRS is a parallelogram.

Learn more :-

ABCD is a rhombus with A = 60° , BC = (3x+5)cm , CD =(6x-10)cm and AC =(3y-1)cm. Find

x and y.

please urgent please

n...

https://brainly.in/question/25624939

3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

https://brainly.in/question/17942233

Answer 2

Answer:

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Step-by-step explanation: