Question

Okay, I am actually really stuck on this question.
"Write an indirect proof proving the two non-right angles of a right triangle measure less than 90°."

Answer 1

This is all I have so far.
If two non-right angles of a right triangle measure more than 90 degrees,

Answer 2

And I don't know what to do next. Can someone please help me?

Answer 3

Actually, I changed it to "Assume two non-right angles of a right triangle measure more tan 90 degrees. "

Answer 4

@zepdrix A little help again please? I know this is the same question, and I thought I had the answer. But is seems that I am still confused. Can you walk me through on how to solve this? I would appreciate it very much.

Answer 5

@jim_thompson5910

Answer 6

"If two non-right angles of a right triangle measure more than 90 degrees"

then what do you know about the sum of those two angles?

Answer 7

Well, the sum of the whole triangle's angles have to equal to 180 degrees.

Answer 8

that's true

Answer 9

So if two of them are already 90 degrees, then there won't be room for another line for the triangle.

Answer 10

good

and it's even worse when the angles are larger than 90 degrees

Answer 11

Okay, so how do I continue this problem?

Answer 12

say you have the two angles x and y

Answer 13

let's make them greater than 90 degrees, so,

x > 90
y > 90

Answer 14

add up the two inequalities (one side at a time) to get

x+y > 90+90
x+y > 180

so this shows you that you go over the 180 degree mark and you don't even make room for a third angle

Answer 15

Okay, so is this a good answer?

Assume two non-right angles of a right triangle measure more than 90 degrees.
The sum of a triangle's angles have to total 180 degrees.
x+y is larger than 90 degrees.
X and Y can't be more than 90 degrees.

Answer 16

Well you skipped a few steps, but you have the right idea

Answer 17

What steps did I skip?

Answer 18

you forgot to define what x and y are

Answer 19

when you say "x+y is larger than 90 degrees", it's hard to know what that means

oh and it should be "x+y is larger than 180 degrees" (not 90)

Answer 20

Ok, so:
Assume two non-right angles of a right triangle measure more than 90 degrees.
The sum of a triangle's angles have to total 180 degrees.
x+y together is larger than 180 degrees.
x and y can't be more than 90 degrees each.

Answer 21

Actually is this better?
Assume two non-right angles of a right triangle measure more than 90 degrees.
The sum of a triangle's angles have to total 180 degrees.
x+y together is larger than 180 degrees.
The sum of two right angles can't be more than 90 degrees.

Answer 22

again you forgot to define x and y

Answer 23

but you pretty much have it

once you get to the contradiction, it invalidates your initial claim that "the angles are larger than 90 degrees"

so that must mean the opposite, the original claim, is true

Answer 24

Okay. And when you mean define x and y, does that mean to give them a number, like x = 91 and y = 91?

Answer 25

(sorry if these questions are stupid - I am only supposed to be in 7th grade and I am taking advanced classes)

Answer 26

x = 91 is a specific example of when you say "x is larger than 90 degrees"

Answer 27

to generalize completely, we say x > 90

Answer 28

so one way you can define x and y is to say

Let x and y be angles of a triangle such that x > 90 and y > 90.

Answer 29

Okay, so this would be good?
Assume two non-right angles of a right triangle measure more than 90 degrees.
The sum of a triangle's angles have to total 180 degrees.
Let x and y be angles of a triangle such that x > 90 and y > 90.
x+y together is larger than 180 degrees.
The sum of two right angles can't be more than 90 degrees.

Answer 30

Good. That's much better.

Answer 31

Thank you very much! I have a few more questions. Would you be willing to help me?

Answer 32

I'll help with 2 more

Answer 33

Okay, thank you!!! :D

Prove that the sides opposite the congruent base angles of a triangle are congruent. Be sure to create and name the appropriate geometric figures.

Answer 34

(These are just questions on a pre-test, but I want to know how to solve them)

Answer 35

Well if it's a pre-test, then it's ok if you don't know the answer. You won't get penalized for getting it wrong.

Answer 36

Getting the wrong answer just means the teacher knows where to focus his/her energy (instead of wasting time on stuff you already know).

Answer 37

Well, would you help me answer another question then?

Answer 38

Here's my other question.

Answer 39

If it's from the pre-test, I can't help you (since I can't help on tests). And again, don't worry. The pre-test is designed to help place you in the proper class so the teacher knows exactly what you understand and don't understand.

Answer 40

So what I'm saying is that you don't have to "ace" it.

Answer 41

Okay, thank you for your help. :)

Answer 42

In fact, I don't think they expect anyone to ace it or else they picked too easy questions.

Answer 43

you're welcome and good luck with it and the rest of the class

Answer 44

Thanks you! :D