In - ABC - AD - DB - AE - EC and - ADE - ACB- Then - ABC is triangle-A- EquilateralB- IsoscelesC- Right angledD- Scalene

The correct option is B IsoscelesFrom Converse of Basic Proportionality theorem, Since AD/DB=AE/EC ∴ DE∥ BC. Given ∠ ADE = ∠ ACB — (1) Since corresponding angl ...

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Standard X

Mathematics

Converse of BPT

In Δ ABC , AD...

Question

In $Δ$ ABC, $\frac{A D}{D B} = \frac{A E}{E C}$ and $∠$ ADE = $∠$ ACB. Then $Δ$ ABC is triangle.

Equilateral

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Isosceles

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Right angled

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Scalene

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Solution

The correct option is B Isosceles
From Converse of Basic Proportionality theorem,
Since $\frac{A D}{D B} = \frac{A E}{E C}$
$∴ D E ∥ B C$ .
Given $∠ A D E = ∠ A C B$ ---- (1)
Since corresponding angles in parallel lines are equal, we have
$\Rightarrow ∠ A D E = ∠ A B C$ -----(2)
From (1) & (2),
$\Rightarrow ∠ A B C = ∠ A C B$
Hence it is an isosceles triangle.

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In Δ ABC, ADDB=AEEC and ∠ ADE = ∠ ACB. Then Δ ABC is triangle.

The correct option is B IsoscelesFrom Converse of Basic Proportionality theorem, Since ADDB=AEEC ∴DE∥BC. Given ∠ADE=∠ACB ---- (1) Since corresponding angles in parallel lines are equal, we have ⇒∠ADE=∠ABC -----(2) From (1) & (2), ⇒∠ABC=∠ACB Hence it is an isosceles triangle.

In $Δ$ ABC, $\frac{A D}{D B} = \frac{A E}{E C}$ and $∠$ ADE = $∠$ ACB. Then $Δ$ ABC is triangle.