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CBSE Class 9 Answered

Show that the line segments joining the mid points of opposite sides of a quardilateral bisect each other.
Asked by pkirankumar4321 | 23 Feb, 2015, 09:18: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
L e t space A B C D space b e space t h e space g i v e n space q u a d r i l a t e r a l. L e t space P comma space Q comma space R space a n d space S space b e space t h e space m i d p o i n t s space o f space t h e space s i d e s comma space A B comma space B C comma space C D space a n d space D A space r e s p e c t i v e l y. W e space n e e d space t o space p r o v e space t h a t space P R space b i s e c t s space Q S N o w space c o n s i d e r space t h e space t r i a n g l e space A C D. S i n c e space S space a n d space R space a r e space t h e space m i d p o i n t s comma space b y space m i d p o i n t space t h e o r e m comma space w e space h a v e comma S R parallel to A C space a n d space S R equals 1 half A C C o n s i d e r space t h e space t r i a n g l e space A B C. S i n c e space P space a n d space Q space a r e space t h e space m i d p o i n t s comma space b y space m i d p o i n t space t h e o r e m comma space w e space h a v e comma P Q parallel to A C space a n d space P Q equals 1 half A C T h u s comma space w e space h a v e comma space P Q equals S R equals 1 half A C space a n d space P Q parallel to S R parallel to A C... left parenthesis 1 right parenthesis S i m i l a r l y comma space w e space c a n space p r o v e space t h a t comma Q R equals S P equals 1 half B D space a n d space Q R parallel to S P parallel to B D... left parenthesis 2 right parenthesis T h u s comma space w e space c a n space s a y space t h a t comma space P Q R S space i s space a space p a r a l l e log r a m. W E space k n o w space t h a t space d i a g o n a l s space o f space a space p a r a l l e log r a m space b i s e c t space e a c h space o t h e r. space T h u s comma space P R space b i s e c t s space Q S.
Answered by Vimala Ramamurthy | 24 Feb, 2015, 09:27: AM

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CBSE 9 - Maths
each side of square field ABCD is 50 m long, length of diagonal field is (route 2 =1.414
Asked by jahnavinehra | 03 Jul, 2022, 11:19: AM
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CBSE 9 - Maths
diagonal AC of a parallelogram ABCD bisects ∆A . i . it biseets ∆C also ii . ABCD is a rhombus
Asked by sanskritiraghudev | 19 Feb, 2022, 09:38: AM
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CBSE 9 - Maths
Why is'nt the angle sum property true for a concave quadrilateral even when we can divide it into two triangles
Asked by katariayash1212 | 16 Jan, 2020, 07:06: PM
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CBSE 9 - Maths
what is quadrilaterals  
Asked by deepakrim74 | 09 Mar, 2019, 08:08: PM
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CBSE 9 - Maths
Why is the angle sum property not applicable to concave quadrilateral?(please explain briefly and if possible with proof and example) Thank you.
Asked by hk.sachdev | 09 Jan, 2019, 08:56: PM
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CBSE 9 - Maths
In a quadrilateral ABCD, the line segments bisecting C and D meet at E. Prove that A + B = 2 CED.
Asked by Topperlearning User | 16 Aug, 2017, 02:17: PM
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CBSE 9 - Maths
In the given figure, PQRS is a quadrilateral in which PQ is the longest side and RS is the shortest side. Prove that R > P.
Asked by Topperlearning User | 16 Aug, 2017, 02:17: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
The angles of a quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.
Asked by Topperlearning User | 16 Aug, 2017, 02:25: PM
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CBSE 9 - Maths
In the given figure, LMNQ is a parallelogram in which L = 75o and QMN = 60o. Find NQM and LQM.
Asked by Topperlearning User | 16 Aug, 2017, 02:19: PM
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CBSE 9 - Maths
In the figure, PQRS is a trapezium in which PQ  SR. if P = 55o and Q = 70o, find R andS.
Asked by Topperlearning User | 16 Aug, 2017, 02:24: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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