In the figure given below- if BC - EF and FG - CD- AE-AB - - AG-GD-GD-AG-AG-AD-CF-AF-

The correct option is C AG/AD In the Δ ABC, EF ∥ BC ∴ AE/AB = AF/AC ......(1) [By BPT] In Δ ACD, FG ∥ CD ∴ AF/AC = AG/AD .......(2) [By BPT] From (1) an ...

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Byju's Answer

Standard IX

Mathematics

Extending BPT for Relation between Bases of Two Triangles

In the figure...

Question

In the figure given below, if BC $∥$ EF and FG $∥$ CD. $\frac{A E}{A B}$ =

$\frac{A G}{G D}$

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$\frac{G D}{A G}$

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$\frac{A G}{A D}$

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$\frac{C F}{A F}$

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Solution

The correct option is C
$\frac{A G}{A D}$

In the $Δ$ ABC,
EF $∥$ BC
$∴$ $\frac{A E}{A B}$ = $\frac{A F}{A C}$ ......(1) [By BPT]

In $Δ$ ACD,
FG $∥$ CD
$∴$ $\frac{A F}{A C}$ = $\frac{A G}{A D}$ .......(2) [By BPT]

From (1) and (2), we get
$\frac{A E}{A B}$ = $\frac{A F}{A C}$ = $\frac{A G}{A D}$
$\Rightarrow \frac{A E}{A B}$ = $\frac{A G}{A D}$

Suggest Corrections

In the figure given below, if BC ∥ EF and FG ∥ CD. AEAB =

The correct option is C AGAD In the Δ ABC, EF ∥ BC ∴ AEAB = AFAC ......(1) [By BPT] In Δ ACD, FG ∥ CD ∴ AFAC = AGAD .......(2) [By BPT] From (1) and (2), we get AEAB = AFAC = AGAD ⇒AEAB = AGAD

In the figure given below, if BC $∥$ EF and FG $∥$ CD. $\frac{A E}{A B}$ =