Question

http://prntscr.com/9731my
http://prntscr.com/9731v8

Answer 1

For #1, this theorem is needed:

Converse of the Pythagorean Theorem, which states that if the sum of the squares of the lengths of two sides of a triangle is equal to the sum of the square of the third side, then the triangle is a right triangle.

Answer 2

Square each side and determine if the square of the longest side = the sum of the squares of the other two sides.

Answer 3

Right off the bat, 4, 4, 4 cannot be sides of a right triangle.

The triangle is equilateral and an equilateral triangle is equiangular.

@kittymeow101 If a triangle has all 3 interior angles the same measure, can one of them be a right angle?

Answer 4

no they can not

Answer 5

Correct. So, that option is out.

Looking at the 1, 2, 3 option, note that one side of a triangle cannot be shorter than the sum of the other two.

1 + 2 = 3 and there is no triangle so that option is out.

Answer 6

true

Answer 7

5.1^2 =

4.1^2 =

3.1^2 =

Time to use the converse of the Pythagorean Theorem.

Square each of the 3 sides of the option.

Does 5.1^2 = 4.1^2 + 3.1^2 ?

Answer 8

Copy and paste 5.1^2 = 4.1^2 + 3.1^2 into the "box" at wolframalpha.com and here is what happens:

http://www.wolframalpha.com/input/?i=5.1%5E2+%3D+4.1%5E2+%2B+3.1%5E2

Answer 9

Click on that and see if the "Wolf" says it is true or false.

Answer 10

so its not correct, which leaves use with option D

Answer 11

Here is the "equation" to test.

Go to wolframalpha.com

Paste this into the entry area: 2.5^2 = 4+1.5^2

See if that relationship is true or false.

Answer 12

the relationship is true which means the answer is D

Answer 13

The answer to #1 is what?

Answer 14

the answer to #1 is D

Answer 15

I agree.

Answer 16

On the second question, it is the Pythagorean theorem again.
But, as the Greeks said it.

The area of the square on the hypotenuse = sum of the areas of the squares on the other two sides.

It amounts to this:

F = D + E

Answer 17

Reading through the options you have to see which ones are equivalent to:

F = D + E.

Answer 18

Think of the first option as:

F - E = D

Is that the same as F = D + E

Answer 19

option D is equivalent to F=D+E

Answer 20

Yes.

What about option A?

F - E = D

Is that the same as F = D + E

Answer 21

no

Answer 22

F - E = D

Add E to both sides:

F = D + E

Answer 23

A and D are both correct options.

Answer 24

ok ty

Answer 25

You are welcome.