Question

abcd is quadrilateral in which p Q r the and s are mid_point of the side ab bc cd and da, ac is a diagonal show that Sr "ac

Answer 1

Given : ABCD is a quadrilateral
P, Q, R and S are midpoint
AC and BD are diagonals

To prove : SR || AC

Proof : In Δ ADC
R is mid point of CD .......... (1)
S is mid point of AD ..........(2)

From (1) & (2)
SR = 1/2 AC
SR || AC [ Midpoint theorem ]
..... Hence Proved


..............._____............... Hope it helps :-).... :-).........

Answer 2

$\huge\tt{\underline{\underline{Question:-}}}$

ABCD is a quadilateral which P,Q,R, and S are the mid points of the sides AB=BC=CD=DA . AC is a diagonal.

• Show that = SRllAC and SR= $\sf\frac{1}{2}$
• PQ = SR
• PQRS is a llgm

$\huge\tt{\underline{\underline{Answer:-}}}$

Given:- In quadilateral ABCD

P,Q,R and S are the mid points of AB=BC=CD=DA.

To prove:- • SR ll AC and SR $\sf\frac{1}{2}$ AC.

• PQ=SR

• PQRS is a llgm.

To prove:- • In ∆DAC,

S and R are the mid points of DA and DC respectively.

Therefore, SR ll AC and SR = $\sf\frac{1}{2}$ AC -------1. (by mid-point theorem)

• In ∆ABC, P and Q are the mid points of AB and BC respectively.

Therefore, PQllAC and PQ= $\sf\frac{1}{2}$--------2. (by mid-point theorem)

From 1. and 2.

PQllSR and PQ = SR

• therefore,PQllSR and PQ=SR

Therefore, PQRS is a llgm.