State true or falseIn the following figure- DE AC and DC AE- then BE - EC - BC - CP-A- TrueB- False

The correct option is A True In the given figure, DE||AC and DC||AP To prove: BE/EC=BC/CP Proof: In Δ BCA ED||CA ∴BE/EC=BD/DA Similarly in Δ BPA DC||AP ∴BC/CP ...

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Byju's Answer

Standard X

Mathematics

Basic Proportionality Theorem

State true or...

Question

State true or false

In the following figure, DE||AC and DC||AE; then $\frac{BE}{EC}=\frac{BC}{CP}$.

True

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False

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Solution

The correct option is A
True

In the given figure,

DE||AC and DC||AP

To prove: $\frac{B E}{E C} = \frac{B C}{C P}$

Proof: In $Δ B C A$

ED||CA

$∴ \frac{B E}{E C} = \frac{B D}{D A}$

Similarly in $Δ B P A$

DC||AP

$∴ \frac{B C}{C P} = \frac{B D}{D A}$

From (i) and (ii),

$\frac{B E}{E C} = \frac{B C}{C P}$

Hence the statement is true.

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State true or false In the following figure, DE||AC and DC||AE; then \(\frac{BE}{EC}=\frac{BC}{CP}\).

The correct option is A True In the given figure, DE||AC and DC||AP To prove: BEEC=BCCP Proof: In ΔBCA ED||CA ∴BEEC=BDDA Similarly in ΔBPA DC||AP ∴BCCP=BDDA From (i) and (ii), BEEC=BCCP Hence the statement is true.

State true or false

In the following figure, DE||AC and DC||AE; then \(\frac{BE}{EC}=\frac{BC}{CP}\).