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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

A B C is a tr...

Question

ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles.

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Solution

It is given that

, and

And.

We have to prove is isosceles.

To prove is isosceles we will prove

For this we have to prove

Now comparing and we have

(Given)

(Common side)

So, by right hand side congruence criterion we have

So (since sides opposite to equal angle are equal)

Hence is isosceles.

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Similar questions

Suppose ABC is a triangle in which BE and CF are respectively the perpendiculars to the sides AC and AB. If BE = CF, prove that triangle ABC is isosceles.

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 $Δ A B E ≅ Δ A C F$

Q. ABC is an isosceles triangle in which the altitudes

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

i . e . Δ A B C i s a n i s o s c e l e s t r i a n g l e .

ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.

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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

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