Answer: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