How to Determine Whether a Triangle is a RIGHT Triangle

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Everybody in this video. I would like to try to answer this question are these these triangles right triangles a right triangle is any triangle that has a 90 degree in it so your first temptation might be well lets grab a protractor and lets try to measure the angles and see if theres a 90 degree angle in it that protractors are useful theyre handy they can give you good approximations. But measuring things is always a little bit inaccurate.
Theres always a little bit of estimation involved so i could bring this over and say yeah. Thats about 90 degrees. But do i know that its exactly 90 could it be actually 89.
It could it be eighty nine point five could it be eighty nine point nine could it be ninety point. One. We dont know for sure at least using a protractor well thankfully.
There is a way that we can know for sure. And that is by using the pythagorean theorem and the pythagorean theorem states that if a triangle is a right triangle then the sum of the squares of the legs is equal to the square of the hypotenuse well so what does that mean let me bring over a different paper here. If we have a right triangle.
Theres our right angle. Then the two sides that meet at that right angle. We call those the legs of the triangle and the side that is across from the right angle is called the hypotenuse and generally we will name the legs size a and b.
And the hypotenuse will call that side c. So in our theorem. Again it says if its a right triangle then the sum of the squares of the legs.
Adds up to the square of the hypotenuse. What does that mean lets take a look at this like the squares of the legs. If this leg right here is a well then this leg squared is going to be a squared.
If this leg is b. Then this leg. Squared is going to be b squared and the hypotenuse squared is the hypotenuse to c.
So. The hypotenuse squared is just simply c squared. So what the pythagorean theorem is saying is that if its a right triangle then a squared plus b.
Squared. The sum of the squares of the legs is equal to the square of the hypotenuse. So thats the pythagorean theorem.
So a little shorter simpler way of stating. This is if we get rid of that long sentence and bring in the equation. Instead.
If a triangle is a right triangle. Then a squared plus b. Squared.
Equals c.

how to tell if a triangle is right-0
how to tell if a triangle is right-0

Squared. This is the sum of the squares of the legs. And thats equal to the square of the hypotenuse well back over to this problem.
Though we dont know for sure that these are right triangles. So were not going to technically be using this pythagorean theorem. What were going to use instead is the converse of the pythagorean theorem.
If we take this pythagorean theorem and turn it around if we turn it backwards. If instead. We say.
If a squared plus b. Squared. Equals c.
Squared. Then the triangle must be a right triangle. So this is the pythagorean theorem up here.
This is the converse of the pythagorean theorem and thats what were going to use were going to check to see if a squared plus b. Squared does indeed equal c. Squared.
Then we know its a right triangle. If a squared plus b. Squared.
Gives us some other number thats not equal to c. Squared. Well say no its not a right triangle.
So lets give that a try well start with this triangle here the legs. If this is a right triangle. The legs are going to be the two shorter sides.
So well call this side a and side b. And this one would be the hypotenuse c. If it is a right triangle.
So lets see if a squared plus b. Squared. Equals c.
Squared. Weve got a is 6. So.
6.

how to tell if a triangle is right-1
how to tell if a triangle is right-1

Squared plus b. Is 11. 11.
Squared is equal to c. Is 13. 13.
Squared. 6. Squared.
6. Times. 6.
Is 36 plus. 11. Squared.
11 times. 11. Is 121 13.
Squared or 13 times. 13. Is 169.
And if i take these two numbers. Now and if i add those together 36 plus 121. Is 157.
And is that equal to our c. Squared. 157.
Is certainly not equal to 169 so we would say a squared plus b squared does not equal c. Squared. So no this is not a right triangle.
Lets try this one using the same logic. The shorter two sides if this were a right triangle. The shorter two sides would be our legs.
So called the shorter two sides a and b. The longest side is going to be our hypotenuse. See if this is a right triangle.
So lets do the same thing does a squared plus b.

how to tell if a triangle is right-2
how to tell if a triangle is right-2

Squared. Equals c. Squared.
So we have. 8. Squared.
Plus. 15. Squared is that equal to 17 squared.
8. Times. 8.
Is 64 15. Times. 15.
Is 225 17 times. 17. Or.
17. Squared. Is 289 take those two 64 plus.
225. Is 289 and sure enough in this case. 289 does equal to 89.
So a squared plus b. Squared is equal to c. Squared.
So. The answer to this one is yes. We have ourselves a right triangle.
And there we know for a fact that one right. There is our right angle. So what we just did was we used the converse of the pythagorean theorem that if a squared plus b.
Squared. Does equal c. Squared.
Then it must be a right triangle. So hopefully. These will be easy problems for you and i hope this video was very helpful.
.

how to tell if a triangle is right-3
how to tell if a triangle is right-3

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