Question

prove the bisector of the vertical angel of an isoscale triangle bisects the base at right angle

Answer 1

It's so simple!

Let the equal angles of the isosceles triangle be x each.

Then the third angle will be 180 - (x + x) = 180 - 2x.

This angle is bisected, isn't it?

So each angle will be (180 - 2x) / 2 = 90 - x.

So consider one small triangle formed by the bisection.

One angle is this 90 - x.

And the other is one among x.

Then the third angle at which the side of the larger main triangle is bisected is,

180 - (x + 90 - x)

180 - 90 = 90

The either sides of the angle which is bisected are equal as the triangle is isosceles. So the angle bisector bisects the side.

∴ The angle bisector bisects the opposite side at 90°.

I've answered it faster. So you may ask me if any doubts.

Thank you. Have a nice day. :-))

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