In given figure $E$ is a point on side $C B$ produced of an isosceles triangle $A B C$ with $A B = A C .$ If $A D ⊥ B C$ and $E F ⊥ A C,$ prove that $△ A B D \sim △ E C F$ .

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Solution

Given $A B = A C$

$∴ ∠ B = ∠ C . . . . . . . . . . . (1)$

In $△ A B D$ and $△ E C F$

$∠ B = ∠ C$ (From 1)

$∠ A D B = ∠ E F C = 90^{o}$ [ $∵ A D ⊥ B C$ and $E F ⊥ A C,$ ]

$∴$ By AA Criterion of Similarity, $△ A B D$ $\sim$ $△ E C F$ $[h e n c e p r o v e d]$

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Similar questions

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

A D ⊥ B C a n d E F ⊥ A C

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(i)

△ A B D \sim △ E C F

(ii)

A B \times E F = A D \times E C

Q. 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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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 $Δ A B D \sim Δ E C F$ .

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In given 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 △ABD∼△ECF.

Given AB=AC∴∠B=∠C...........(1) In △ABD and △ECF∠B=∠C (From 1)∠ADB=∠EFC=90o [∵AD⊥BC and EF⊥AC,]∴ By AA Criterion of Similarity, △ABD ∼ △ECF [henceproved]

In given figure $E$ is a point on side $C B$ produced of an isosceles triangle $A B C$ with $A B = A C .$ If $A D ⊥ B C$ and $E F ⊥ A C,$ prove that $△ A B D \sim △ E C F$ .

Given $A B = A C$

$∴ ∠ B = ∠ C . . . . . . . . . . . (1)$

In $△ A B D$ and $△ E C F$

$∠ B = ∠ C$ (From 1)

$∠ A D B = ∠ E F C = 90^{o}$ [ $∵ A D ⊥ B C$ and $E F ⊥ A C,$ ]

$∴$ By AA Criterion of Similarity, $△ A B D$ $\sim$ $△ E C F$ $[h e n c e p r o v e d]$