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Find the angles respectively of a ∆PQR. For each of the following cases, state whether EF || QR: (i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cmKoi mujhse friendship karega :) |
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Answer» Explanation: E and F are two points on side PQ and PR in △PQR. (i) PE=3.9 cm, EQ=3 cm and PF=3.6 cm, FR=2.4 cm Using BASIC proportionality theorem, ∴ EQ PE
= 3 3.9
= 30 39
= 10 13
=1.3 FR PF
= 2.4 3.6
= 24 36
= 2 3
=1.5 EQ PE
= FR PF
(II) PE=4 cm, QE=4.5 cm, PF=8 cm, RF=9 cm Using Basic proportionality theorem, ∴ QE PE
= 4.5 4
= 45 40
= 9 8
RF PF
= 9 8
QE PE
= RF PF
So, EF is parallel to QR. (iii) PQ=1.28 cm, PR=2.56 cm, PE=0.18 cm, PF=0.36 cm Using Basic proportionality theorem, EQ=PQ−PE=1.28−0.18=1.10 cm FR=PR−PF=2.56−0.36=2.20 cm EQ PE
= 1.10 0.18
= 110 18
= 55 9
... (i) FR PE
= 2.20 0.36
= 220 36
= 55 9
... (ii) ∴ EQ PE
= FR. PF
So, EF is parallel to QR. |
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