sorry for the fuzzy display. please help...OA is A.
from 1) i see that all the segments correspond with each other. BQ=CR=DS=AP, thus QC=RD=AS=BP because all sides of the square are equal. but knowing that, how do we know that these line segments QS and PR are equal?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
DS prep
This topic has expert replies
-
gabriel
- Legendary Member
- Posts: 986
- Joined: Wed Dec 20, 2006 11:07 am
- Location: India
- Thanked: 51 times
- Followed by:1 members
.. bcoz if they werent equal they wuldnt have made equal intercepts on the oppsite sides .. that is they wuldnt have divided the sides in equal ratios ... and this true only bcoz the figure is a square ..bww wrote:sorry for the fuzzy display. please help...OA is A.
from 1) i see that all the segments correspond with each other. BQ=CR=DS=AP, thus QC=RD=AS=BP because all sides of the square are equal. but knowing that, how do we know that these line segments QS and PR are equal?
-
Cybermusings
- Legendary Member
- Posts: 559
- Joined: Tue Mar 27, 2007 1:29 am
- Thanked: 5 times
- Followed by:2 members
Since BQ=CR=SD=AP; it’s clear that QC=RD=SA=BP
This also proves that QR=RS=PS=QP (they all represent the hypotenuse of 4 triangles)
All the four triangles would be congruent Triangle CQR, RSD, PAS and PBQ…Hence all angles and sides of PQRS will be equal…thus it becomes a square….hence PR = QS
This also proves that QR=RS=PS=QP (they all represent the hypotenuse of 4 triangles)
All the four triangles would be congruent Triangle CQR, RSD, PAS and PBQ…Hence all angles and sides of PQRS will be equal…thus it becomes a square….hence PR = QS
