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ICSE Class 10 Answered

Please solve this 
question image
Asked by dr_pradip27121972 | 21 Sep, 2018, 09:35: AM
answered-by-expert Expert Answer
All constuctions are in RED
Join DP
now we have to prove DP || BQ
in triangle DAP and BCQ
angle DAP = angle BCQ.....opp angles of ||gm
AD=BC and AP =QC ......Opp sides of ||gm
so both the triangles are congruent by SAS
so angle APD = angle CQB.....C.P.C.T.
now,
PB||QC and BQ transversal
so, angle CQB = angle PBQ
so angle APD = angle PBQ
thus PB||QC....converse of corresponding angle test
In tri ABS 
PT||BS and P is the mid point so
T is also the mid point of AS
AT=TS=10
in tri CTD
Q is the mid point and DT||QS
so
begin mathsize 18px style CT over CS equals 2 fraction numerator begin display style CS plus TS end style over denominator begin display style CS end style end fraction equals 2 CS space equals space 10 end style
 
We have to prove that TR = RS
we can prove triangles APR and CQR equal by ASA test AP = QC and corresponding angles
from that we can say PR = RQ ...cpct
so in tri TPR and SQR
we have PR = RQ and alternate and vertcally opposite angles
so tri TPR and SQR are congruent by ASA test and TR = RS ....cpct
TR = RS = 5
now 
Q1
begin mathsize 18px style increment CQR space and space increment SCQ space have space common space base so fraction numerator increment CQR over denominator increment SCQ end fraction equals RY over SZ now comma increment CZS space tilde space increment CYR space by space AA space test RY over SZ equals CR over CS equals fraction numerator CS plus RS over denominator CS end fraction equals 15 over 10 fraction numerator increment CQR over denominator increment SCQ end fraction equals 15 over 10 end style
Error converting from MathML to accessible text.

begin mathsize 18px style fraction numerator square ASQD over denominator square ABCD end fraction equals fraction numerator square ABCD minus increment ABC minus increment SQC over denominator square ABCD end fraction increment ABC equals 1 half square ABCD..... left parenthesis 1 right parenthesis increment RQC equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction increment ADC increment RQS plus increment SQC equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction increment ADC fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction increment SQC plus increment SQC equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction increment ADC........ fraction numerator increment SCQ over denominator increment RSQ end fraction equals 10 over 5 fraction numerator begin display style 3 end style over denominator begin display style 2 end style end fraction increment SQC equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction open parentheses 1 half square ABCD close parentheses increment SQC equals 1 over 6 square ABCD..... left parenthesis 2 right parenthesis resub space 1 space and space 2 space in space fraction numerator square ASQD over denominator square ABCD end fraction equals fraction numerator square ABCD minus increment ABC minus increment SQC over denominator square ABCD end fraction end style


Answered by Arun | 25 Sep, 2018, 12:53: PM

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