Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

ABCD is a quadrilateral in which P, Q, R and S are mid points of AB, BC, CD and DA respectively. Show that PQRS is a parallelogram.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Construction : Join AC

In DAC,

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

By mid point theorem

SR || AC and SR = ...(1)

Similarly in BAC,

PQ || AC and PQ = ...(2)

From (1) and (2),

SR || PQ and SR = PQ

Hence PQRS is a parallelogram.

Answered by | 04 Jun, 2014, 03:23: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
the line segment joining the midpoints of two sides of a triangle is parallel to the third side
Asked by vineetyadav77050 | 25 Jul, 2021, 05:45: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Q. 7
question image
Asked by Rayeesa | 04 Jun, 2018, 09:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
M is the mid point of side PQ of a parallelogram PQRS. A line through Q parallel to PS meets SR at N and PS produced at L. Prove that (i) PL = 2QR (ii) QL = 2QN.
Asked by Topperlearning User | 11 Aug, 2017, 11:58: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
State the mid point Theorem.
Asked by Topperlearning User | 11 Aug, 2017, 12:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that the triangles formed by joining in pairs, the mid points of the three sides of a triangle are congruent to each other.
Asked by Topperlearning User | 11 Aug, 2017, 11:59: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that the line drawn through the mid point of one side of a triangle, parallel to another side, intersects the third side at its mid point.
Asked by Topperlearning User | 11 Aug, 2017, 12:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In PQR, A, B and C are the mid points of QR, RP and PQ respectively. If the lengths of sides PQ, QR and RP are 7 cm, 8 cm and 9 cm respectively, find the perimeter of ABC. 
Asked by Topperlearning User | 11 Aug, 2017, 12:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that the triangle formed by joining the mid points of the sides of an isosceles triangle is an isosceles triangle.
Asked by Topperlearning User | 11 Aug, 2017, 11:52: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In the figure, E is the mid-point of side AD of a trapezium ABCD with AB  CD. A line through E parallel to AB meets BC in F. Show that F is the mid point of BC.
Asked by Topperlearning User | 11 Aug, 2017, 11:56: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
M, N and P are the mid points of AB, AC and BC respectively. If MN = 3 cm, NP = 3.5 cm and MP = 2.5 cm. Calculate BC, AB and AC.
Asked by Topperlearning User | 11 Aug, 2017, 11:59: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×