$A B C$ is a triangle whose altitudes $B E$ and $C F$ to sides $A C$ and $A B$ , respectively, are equal. Which of these conditions is not required to prove $△ A B E ≅ △ A C F ?$

∠ B = ∠ C

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∠ B A E = ∠ F A C

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∠ A F C = ∠ A E B

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B E = C F

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Solution

The correct option is A $∠ B = ∠ C$
From $△ A B E$ & $△ A C F$
$∠ A E B = ∠ A F C$
$B E = C F$
given $△ A B E ≅ △ A C F$
$∠ B A E = ∠ F A C, ∠ A F C = ∠ A E B$
So, the condition $∠ B = ∠ C$ is not required.

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Similar questions

Q. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that triangle ABE equal and congruent to triangle ACF

ABC is an isosceles triangle in which altitudes $B E$ and $C F$ are drawn to equal sides $A C$ and $A B$ respectively. Show that $Δ A B E ≅ Δ A C F$

$A B C$ is a triangle in which altitudes $B E$ and $C F$ to sides $A C$ and $A B$ are equal (see Fig.). Show that
(i) $△ A B E ≅ △ A C F$
(ii) $A B = A C$ , i.e., $A B C$ is an isosceles triangle.

Q. Question 4 (i)
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
(i)

Δ A B E ≅ Δ A C F

A B C

is triangle in which altitudes

B E

and

C F

to sides

A C

and

A B

are equal. How many of the following are true:
(a)

Δ A B E ≅ Δ A C F

(b)

A B = A C

, i.e., is an isosceles triangle.

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ABC is a triangle whose altitudes BE and CF to sides AC and AB, respectively, are equal. Which of these conditions is not required to prove △ABE≅△ACF?

The correct option is A ∠B=∠CFrom △ABE & △ACF∠AEB=∠AFCBE=CFgiven △ABE≅△ACF∠BAE=∠FAC,∠AFC=∠AEBSo, the condition ∠B=∠C is not required.

$A B C$ is a triangle whose altitudes $B E$ and $C F$ to sides $A C$ and $A B$ , respectively, are equal. Which of these conditions is not required to prove $△ A B E ≅ △ A C F ?$

The correct option is A $∠ B = ∠ C$
From $△ A B E$ & $△ A C F$
$∠ A E B = ∠ A F C$
$B E = C F$
given $△ A B E ≅ △ A C F$
$∠ B A E = ∠ F A C, ∠ A F C = ∠ A E B$
So, the condition $∠ B = ∠ C$ is not required.