Question

if u need help come here

Answer 1

whats your question

Answer 2

can you write an indirect proof proving only one angel of an obtuse triangle is greater than 90 degree?

Answer 3

90 degree is a right angle so put that as a triangle

Answer 4

Indirect proof is a proof of contradiction. List the things you know abot an obtuse triangle

- It's a triangle so must have interior angles that total 180º

a+b+c=180º


- An obtuse must have one angle that is larger than 90º and less than 180º

90º<a<180º or 90º<b<180º or 90º<c<180º


Now you assume that at least 2 angles of the triangle have angles greater than 90º

Can you write an equation or expression for that part?

Answer 5

it's 90º<a<180º and 90º<b<180º - the inequalities open to the right to make it say "90 degrees is less than a, a is less than 180 degrees," but I knew what you meant. The AND was the important part)

So if a AND b are both greater than 90º, what happens to c when we try to sum up the angles

(a+b)+c=180

Answer 6

c has to be less than 90 degree?

Answer 7

You start with the things that must be true for every triangle

a
b
c
Reply Using Drawing


For every triangle a+b+c=!180º


For every obtuse triangle 90º<a<180º


Assumption: both a and b are greater than 90º 90º<a<180º ; 90º<b<180º


If true 180º<a+b<360º


Then for (a+b)+c=!180º c<0


This makes no physical sense. Thus only 90º<a<180º can be true. There exists only one obtuse angle in an obtuse triangle. QED.



the equals sign means "must be equal to." You could also use the triple equals sign

Answer 8

i'm sorry i confused.
okay so i have to start by assuming the opposite so , at least 1 or more equals to 90 degrees right?

Answer 9

right

Answer 10

Assume the contrary: A triangle exists that has two obtuse angles.

The measure of an obtuse angle is > 90 degrees
The sum of the angles of this triangle will therefore be m Angle A + m Angle B + m Angle C > 180 degrees
The sum of the angles of a triangle = 180 degrees

CONTRADICTION

Therefore, a triangle in the cartesian plane has at most one obtuse angle. (Note - a triangle can have more than one obtuse angle in non-cartesian geometries. Think about a triangle on the globe....)

Answer 11

Assume the contrary: A triangle exists that has two obtuse angles.

The measure of an obtuse angle is > 90 degrees
The sum of the angles of this triangle will therefore be m Angle A + m Angle B + m Angle C > 180 degrees
The sum of the angles of a triangle = 180 degrees

CONTRADICTION

Therefore, a triangle in the cartesian plane has at most one obtuse angle. (Note - a triangle can have more than one obtuse angle in non-cartesian geometries. Think about a triangle on the globe....)

Answer 12

so i can just just put this
The measure of an obtuse angle is > 90 degrees
The sum of the angles of this triangle will therefore be m Angle A + m Angle B + m Angle C > 180 degrees
The sum of the angles of a triangle = 180 degrees

Answer 13

yes

Answer 14

alright thank you so much

Answer 15

np

Answer 16

@Tal_Tal

Answer 17

need help