In the following figure- DE-AC and DC-AP- then nbsp-BE-EC- nbsp- BC-EC-BC-AC-BC-CP-BD-AC-

The correct option is C BC/CP 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 nbsp; nbsp;....(i) Similarl ...

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Byju's Answer

Standard IX

Mathematics

Extending BPT for Relation between Bases of Two Triangles

In the follow...

Question

In the following figure, DE||AC and DC||AP; then $\frac{B E}{E C} =$ ___

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

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$\frac{B C}{A C}$

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

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$\frac{B D}{A C}$

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Solution

The correct option is C
$\frac{B C}{C P}$

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

$∴ \frac{B E}{E C} = \frac{B D}{D A}$ ....(i)

Similarly in $Δ B P A$

DC||AP

$∴ \frac{B C}{C P} = \frac{B D}{D A}$ ......(ii)

From (i) and (ii),

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

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Similar questions

In the following figure, DE // AC and DC // AP. Prove that: $\frac{B E}{E C} = \frac{B C}{C P} .$

Q. In the given figure, DB ⊥ BC, DE ⊥ AB and AC ⊥ BC.
Prove that

\frac{B E}{D E} = \frac{A C}{B C} .

Q. In given figure,

D E | | A C

and

D C | | A P

. Prove that

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

Q. In the following figure,

D E ∥ A C

and

D C ∥ A P

. Prove that

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

In the given figure, DE || AC, DC || AP, BC = 2 cm, and BP = 6 cm. Find the value of EC/BE.

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In the following figure, DE||AC and DC||AP; then BEEC= ___

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

In the following figure, DE||AC and DC||AP; then $\frac{B E}{E C} =$ ___