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Standard X

Mathematics

Similar Polygons

In the follow...

Question

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

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Solution

It is given that ABC is an isosceles triangle.

∴ AB = AC

⇒ ∠ABD = ∠ECF

In ΔABD and ΔECF,

∠ADB = ∠EFC (Each 90°)

∠ABD = ∠ECF (Proved above)

∴ ΔABD ∼ ΔECF (By using AA similarity criterion)

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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

⊥

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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

Q. E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If

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and

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, prove that

Δ A B D \sim Δ E C F .

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

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prove that

△ A B D \sim △ E C F

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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

It is given that ABC is an isosceles triangle. ∴ AB = AC ⇒ ∠ABD = ∠ECF In ΔABD and ΔECF, ∠ADB = ∠EFC (Each 90°) ∠ABD = ∠ECF (Proved above) ∴ ΔABD ∼ ΔECF (By using AA similarity criterion)

It is given that ABC is an isosceles triangle.

∴ AB = AC

⇒ ∠ABD = ∠ECF

In ΔABD and ΔECF,

∠ADB = ∠EFC (Each 90°)

∠ABD = ∠ECF (Proved above)

∴ ΔABD ∼ ΔECF (By using AA similarity criterion)