Question

In a geometry class, the students were asked to prove the theorem below by contradiction:

Theorem: A triangle has at the most one obtuse angle.

Heather begins the proof with an assumption. Which statement will she most likely use as an assumption?

Let two angles of a triangle be obtuse.

Let each angle of a triangle be acute.

Let only one angle of a triangle be obtuse.

Let two angles of a triangle be right.

Answer 1

@phi

Answer 2

@ganeshie8

Answer 3

prove the theorem below by *contradiction*

A triangle has at the most one obtuse angle.

which of the choices would contradict this statement (make it false)?

Answer 4

isnt C wrong right

Answer 5

@phi

Answer 6

I guess you have to understand what the statement means
A triangle has at the most one obtuse angle.

what kind of triangle would make that statement false ?
say it in words.

Answer 7

right?

Answer 8

what kind of triangle would make that statement false ?
say it in words.

Answer 9

Let two angles of a triangle be obtuse. ?

Answer 10

Yes. If a triangle has TWO angles that are obtuse, that contradicts
a triangle can have AT MOST ONE obtuse angle.

to prove by contradiction
you pick the statement that contradicts what you want to prove

Answer 11

So its A?

Answer 12

@phi

Answer 13

yes

Answer 14

ty