ICSE Class 10 Answered
Please solve this
Asked by dr_pradip27121972 | 21 Sep, 2018, 09:35: AM
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
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
Answered by Arun | 25 Sep, 2018, 12:53: PM
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