In the following figure- if DP -5 cm - DE -15 cm - DQ -6 cm and DF -18 cm- thenA- DP - DFB- P Q - EFC- P Q EFD- DE - DQ

The correct option is C PQ ∥ EF As per the question: DP = 5 cm, DE = 15 cm, DQ = 6 cm and DF = 18 cm Here, DP/DE = 5 cm/15 cm=1/3 and DQ/DF =6 cm/18 cm = 1/3 i ...

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Standard X

Mathematics

Basic Proportionality Theorem

In the follow...

Question

In the following figure, if DP = 5 cm, DE = 15 cm, DQ = 6 cm and DF = 18 cm, then

$P Q = E F$

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$P Q ∥ E F$

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DP = DF

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DE = DQ

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Solution

The correct option is B
$P Q ∥ E F$

As per the question:

DP = 5 cm, DE = 15 cm, DQ = 6 cm and DF = 18 cm

Here, $\frac{D P}{D E} = \frac{5 c m}{15 c m} = \frac{1}{3}$
and $\frac{D Q}{D F} = \frac{6 c m}{18 c m} = \frac{1}{3}$
i.e. in $Δ D E F, \frac{D P}{D E} = \frac{D Q}{D F}$
$∴$ By the converse of Basic proportionality Theorem,
$P Q ∥ E F$

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P

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In the following figure, if DP = 5 cm, DE = 15 cm, DQ = 6 cm and DF = 18 cm, then

The correct option is B PQ∥EF As per the question: DP = 5 cm, DE = 15 cm, DQ = 6 cm and DF = 18 cm Here, DPDE=5 cm15 cm=13 and DQDF=6 cm18 cm=13 i.e. in ΔDEF,DPDE=DQDF ∴ By the converse of Basic proportionality Theorem, PQ∥EF