Question

Can the altitude to the base of an isosceles triangle be longer than the leg of the triangle?

Answer 1

Please explain with a diagram.

Thanks! \(\Large\color{magenta}{\heartsuit}\)

Answer 2

@jim_thompson5910 @zepdrix @iambatman

Answer 3

this is a right triangle?

Answer 4

It is an isosceles triangle. No other information is given.

Answer 5

here are 2 examples of isosceles triangles

Answer 6

draw in the altitude or height



does the height look longer than the congruent legs?

Answer 7

I have drawn an isosceles triangle and as you can see the altitude is greater than the base
there are not restrictions for it

Answer 8

@jim_thompson5910 Not on all of them, no.

Answer 9

2 different situations, where the altitude to the base is greater
and lower than the base

Answer 10

So it could be longer?

Answer 11

focus on this right triangle

Answer 12

the leg of the isosceles triangle is now the hypotenuse of that triangle I highlighted

Answer 13

I'm not getting it.. is it longer?? o-O

Answer 14

the hypotenuse is always the longest side

Answer 15

so the altitude of the isosceles triangle is never longer than the leg of the isosceles triangle

Answer 16

Never? No matter the size?

Answer 17

correct, the altitude is either equal to the leg or smaller than the leg

it's only equal to the leg when we have an isosceles right triangle

Answer 18

Okay, that makes sense, now..
\(\Large\bf\color{magenta}{\bigstar~}\color{blueviolet}{Thanks!~}\color{magenta}{~\bigstar}\)

Answer 19

you're welcome