Question

abcd is a quadrilateral in which p,q,r,s are mid points of the side AB,BC,CD,and DA .AC is a diagonal show that
1. SR is parallel to AC and half of AC
2. PQ is equal SR
3. PQRS is a parallelogram​

Answer 1

Answer:

sr is parrel to ac(by mid point theorem)

sr=1/2AC(by mid point theorem

Answer 2

Answer:

Step-by-step explanation:

the sides AB=BC=CD=DA . AC is a diagonal.

Show that = SRllAC and SR=

PQ = SR

PQRS is a llgm

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 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 = AC -------1. (by mid-point theorem)

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

Therefore, PQllAC and PQ= --------2. (by mid-point theorem)

From 1. and 2.

PQllSR and PQ = SR

• therefore,PQllSR and PQ=SR

Therefore, PQRS is a llgm.

Thank you