E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If $A D ⊥ B C$ and $E F ⊥ A C$ , prove that $Δ A B D \sim Δ E C F .$

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Solution

It is given that ABC is an isosceles triangle.
$∴ A B = A C$
$\Rightarrow ∠ A B D = ∠ E C F$
$I n Δ A B D a n d Δ E C F$
$∠ A D B = ∠ E F C (E a c h 90 °)$
$∠ B A D = ∠ C E F (P r o v e d a b o v e)$
$∴ Δ A B D Δ E C F (B y u s i n g A A s i m i l a r i t y c r i t e r i o n)$

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Similar questions

Q. In the following figure, E is a point on side CB produced, of an isosceles triangle ABC, with AB = AC. If AD

⊥

BC and EF

⊥

AC, prove that

Δ A B D \sim Δ E C F

Question 11
In the following figure, E is a point on side CB produced, of an isosceles triangle ABC, with AB = AC. If AD $⊥$ BC and EF $⊥$ AC, prove that $Δ A B D \sim Δ E C F$ .

Q. Question 11
In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD

⊥

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⊥

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Δ A B D \sim Δ E C F

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD ∼ ΔECF

Q. In given figure

E

is a point on side

C B

produced of an isosceles triangle

A B C

with

A B = A C .

A D ⊥ B C

and

E F ⊥ A C,

prove that

△ A B D \sim △ E C F

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E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If AD⊥BC and EF⊥AC, prove that ΔABD∼ΔECF.

It is given that ABC is an isosceles triangle.∴AB=AC⇒∠ABD=∠ECFIn ΔABD and ΔECF∠ADB=∠EFC (Each90°)∠BAD=∠CEF (Proved above)∴ΔABD ΔECF (By using AA similarity criterion)

E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If $A D ⊥ B C$ and $E F ⊥ A C$ , prove that $Δ A B D \sim Δ E C F .$

It is given that ABC is an isosceles triangle.
$∴ A B = A C$
$\Rightarrow ∠ A B D = ∠ E C F$
$I n Δ A B D a n d Δ E C F$
$∠ A D B = ∠ E F C (E a c h 90 °)$
$∠ B A D = ∠ C E F (P r o v e d a b o v e)$
$∴ Δ A B D Δ E C F (B y u s i n g A A s i m i l a r i t y c r i t e r i o n)$