Request a call back

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

CBSE Class 9 Answered

ABCD is quadrilateral in which P Q R S are mid points of the sides AB BC CD DA. AC is diagonal. show that SR is parallel to AC and SR= 1half 2 AC
Asked by aksharapatni | 30 Nov, 2023, 01:12: PM
answered-by-expert Expert Answer
Figure shows the quardilateral ABCD . P, Q, R and S are mid points of sides AB, BC, CD and DA respectively.
 
Let us consider Δ ADC and ΔSDR .
 
DS/DA = DR/DC = 1/2
 
begin mathsize 14px style angle end styleADC is common to both triangle .
 
SAS Similarity theorem states that if the two sides of a triangle are in the same proportion to the two sides of another triangle,
and the angle included by the two sides in both the triangles are same, then two triangles are similar.
 
Hence Δ ADC and ΔSDR are similar triangles .
 
begin mathsize 14px style angle end styleDSR = begin mathsize 14px style angle end styleDAC ( corrseponding angles are equal )
begin mathsize 14px style angle end styleDRS = begin mathsize 14px style angle end styleDCA ( corrseponding angles are equal )
Hence SR is parallel to AC.
 
By property of similar triangles
 
SR/AC = DS/ DA = DR/DC = 1/2
Answered by Thiyagarajan K | 30 Nov, 2023, 07:54: PM
CBSE 9 - Maths
Asked by borakartike2 | 29 Dec, 2023, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by bathinisampath | 05 Apr, 2022, 10:52: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by bathinisampath | 05 Apr, 2022, 10:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by abdulsamad82007 | 15 Jun, 2021, 12:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by rjaat7623 | 28 Feb, 2021, 10:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by Narendravignesh | 09 Oct, 2019, 06:02: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by arajeevshashank | 25 Sep, 2019, 12:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by Vats4334 | 12 Sep, 2019, 05:54: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×