Request a call back

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

ICSE Class 9 Answered

Prove that a line joining the mid points of the parallel sides of a trapezium divides it into two equal parts
Asked by aswani1617 | 18 Sep, 2018, 11:02: PM
answered-by-expert Expert Answer
G
 
Given : ABCD is a Trapezium
Point H and G are the mid point of parallel sides.
 
Construction: AE and BF are the height of the trapezium.
 
To prove : Area of begin mathsize 16px style square end styleAHGD = Area of begin mathsize 16px style square end styleHBCG
 
Let us assume that The given Trapezium is an isosceles Trapezium, with AD = BC
 
Here,
AH = HB and DG = GC      ....since Point H and G are the mid-point of AB and CD.
 
 begin mathsize 16px style square end styleAHGE and  begin mathsize 16px style square end styleBHGF are rectagle.
(since AE = BF ..since AB || CD and  AE and BF are perpendicular to DG and GC respectively)
 
EG = AH .......(sides of a reactangle)
HB = GF ......(side of a rectangle)
Therefore Area of a begin mathsize 16px style square end styleAHGE =  Area of a begin mathsize 16px style square end styleBHGF ....(i)
 
In ΔADE and ΔBFC
 
AE = BF
AD = BC
and angleAED =  angleBFC = 900   
Therefore ΔADE  approximately equal to ΔBFC   ...(RHS )
Therefore ΔADE = ΔBFC.......(ii)
 
Area of a begin mathsize 16px style square end styleAHGD = ΔADE +begin mathsize 16px style square end styleAHGE and 
Area of a begin mathsize 16px style square end styleBHCG = ΔBFC + begin mathsize 16px style square end styleBHGF 
from (i) and (ii), we get
Area of begin mathsize 16px style square end styleAHGD = Area of begin mathsize 16px style square end styleHBCG
Answered by Yasmeen Khan | 19 Sep, 2018, 02:37: PM
ICSE 9 - Maths
Asked by tripathiaditya881 | 01 Mar, 2024, 12:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by renukhanna180 | 23 Feb, 2024, 08:49: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by pallachulla | 07 Feb, 2024, 07:50: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by kaberipanda87 | 06 Feb, 2024, 12:29: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by kumarhartish4 | 05 Feb, 2024, 03:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by saurabhgurjarsaurabh55 | 02 Feb, 2024, 07:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by gowthammmi123 | 30 Jan, 2024, 08:19: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by adibulhassansyed12 | 23 Jan, 2024, 11:18: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 9 - Maths
Asked by dp1744825 | 17 Jan, 2024, 08:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×