If in a ABC- a line DE - BC- intersects AB in D and AC in E- then ABAD-ACAE

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Condition for Two Lines to Be Parallel

If in a ABC...

Question

If in a $△ A B C$ , a line $D E | | B C$ , intersects $A B$ in $D$ and $A C$ in $E$ , then $\frac{A B}{A D} = \frac{A C}{A E}$

True

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False

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Solution

The correct option is A True
In $Δ A B C$ and $Δ A D E$ :

$∠ B = ∠ D$ .......[corresponding angles]

$∠ C = ∠ E$ .......[corresponding angles]

$∠ A = ∠ A$ ......[common]

Hence $Δ A B C \sim Δ A D E$ ...........[By $A A A$ criteria]

Also in similar triangles ratio of sides area eqaual.

So,
$\frac{A B}{A D} = \frac{A C}{A E}$ .

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If in a △ABC, a line DE||BC, intersects AB in D and AC in E, then ABAD=ACAE

The correct option is A TrueIn ΔABC and ΔADE:∠B=∠D.......[corresponding angles]∠C=∠E.......[corresponding angles]∠A=∠A......[common]Hence ΔABC∼ΔADE...........[By AAA criteria]Also in similar triangles ratio of sides area eqaual.So,ABAD=ACAE.

If in a $△ A B C$ , a line $D E | | B C$ , intersects $A B$ in $D$ and $A C$ in $E$ , then $\frac{A B}{A D} = \frac{A C}{A E}$