Pqrs is a parallelogram in which a, b, c and d are mid points of its sides respectively. prove that abcd is a parallelogram?

Step-by-step explanation:

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

i) In △DAC , S is the mid point of DA and R is the mid point of DC. Therefore, SR∥AC and SR=  

2

1

AC.By mid-point theorem.

(ii) In △BAC , P is the mid point of AB and Q is the mid point of BC. Therefore, PQ∥AC and PQ=  

2

1

AC.By mid-point theorem. But from (i) SR=  

2

1

AC therefore PQ=SR

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

i) In △DAC , S is the mid point of DA and R is the mid point of DC. Therefore, SR∥AC and SR=  

2

1

AC.By mid-point theorem.

(ii) In △BAC , P is the mid point of AB and Q is the mid point of BC. Therefore, PQ∥AC and PQ=  

2

1

AC.By mid-point theorem. But from (i) SR=  

2

1

AC therefore PQ=SR

(iii)  PQ∥AC & SR∥AC therefore  PQ∥SR and PQ=SR. Hence, a quadrilateral with opposite sides equal and paralle is a parallelogram. Therefore PQRS is a parallelogram.

THANKS  

0

0.0

(0 votes)

Log in to add comment

Find Math textbook solutions?

SEE ALL

Class Class 12

Class Class 11

Class Class 10

Class Class 9

Class Class 8

Class Class 7

Class Class 6

Class Class 5

Class Class 4

Class Class 3

Class Class 2

Class Class 1

NCERT Class 9 Mathematics

619 solutions

NCERT Class 8 Mathematics

815 solutions

NCERT Class 7 Mathematics

916 solutions

NCERT Class 10 Mathematics

721 solutions

NCERT Class 6 Mathematics

1230 solutions

ML Aggarwal - Understanding Mathematics - …

2080 solutions

Xam Idea Mathematics 10

2278 solutions

ML Aggarwal - Understanding Mathematics - …

2090 solutions

R S Aggarwal - Mathematics Class 8

1963 solutions

R D Sharma - Mathematics 9

2199 solutions

SEE ALL

Advertisement

Still have questions?

FIND MORE ANSWERS

ASK YOUR QUESTION

New questions in Math

3) In the figure B = 90° A= C = 45 , AB = 12cm - Find AC.

the length and the breadth of a rectangular piece of land are in the ratio 5:2.If the total cost of fencing it at rs.12.5per meter is rs.25000, find i …

4. Find the zeroes of the polynomial a. P(x)=3x-2 b. P(x)=(x-2)2-(x+2)

evaluate the following expression [250-{(84÷3) +(19*7) "-43}]"

The number of zeroes in the square of 129000

= - 2:1. Use the identity (x + a)(x + b) = x2 + (a + b)x + ab to find the following products: b + + (a) (2x + 54)(2x + 36) (b) (4x + 5)(4x - 1) f the …

what should be multiplied by 16 to get 2000

If $18\sqrt 8-8\sqrt{18}=\sqrt n$, what is $n$?

10 सेमी लांब, 6 सेमी रुंदी व 4 सेमी उंचीच्या खोक्यात 2 सेमी भुजा असलेले जास्तीत जास्त किती घनाकृती ठोकळे बसवता येतील? A) 30 B) 15 C) 40 D) 45

In which of the following x and y vary directly with each other for each direct variation state the constant of variation

$18 was the price of the t-shirt

step-by-step explanation: