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Triangles Made Easy: Angles, Ratios & Classifications Explained!
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May 7, 2025
In this video, we break down everything you need to know about triangles in a fun and easy-to-follow way! Whether you’re just starting geometry or need a refresher, this lesson covers it all—from the definition of a triangle to solving for unknown angles and classifying triangles based on their sides and angles. What You’ll Learn: What makes a triangle a triangle (and why “tri” means 3!) The sum of interior angles of a triangle How to solve for a missing angle using subtraction from 180° Understanding and solving angle ratio problems The difference between acute, right, obtuse, and straight angles Triangle types: scalene, isosceles, and equilateral Classifying triangles by both angles and sides ✏️ Perfect for middle school, high school, or homeschool students learning geometry. 👀 Watch until the end for practice examples and clear visuals! 👍 If this helped you, don’t forget to like, subscribe, and drop your questions in the comments below!
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0:00
so what do we need to know about
0:01
triangles we need to know about
0:03
triangles so you don't meet them like
0:05
there's a lot of things with triangles
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right we're going to talk about the
0:08
pagan when you go to algebra one you
0:11
know you're going to talk about it we're
0:12
going to talk about sign cosine how to
0:14
find the measure of an angle and all of
0:16
that stuff geometry is actually really
0:19
practical so I I think it's probably one
0:21
of the things that you may want to like
0:23
look into a lot cuz this is I like I
0:26
like geometry some of it not all of it i
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don't like I don't really like poop yeah
0:35
you didn't flinch that much all right so
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we're going to talk about triangle right
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now a triangle is pretty much formed by
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doing what by colliding three line
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segment right here how many segments do
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I have here three three segment i have
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this segment i have this segment and I
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have this segment so if you put them
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together you got what you call a
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triangle why what does this the word T r
1:02
I stand for tri is what three three
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right triangle that means what does that
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mean three what three angles so we have
1:10
three angles here we have X we have Y
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and we have Z and all these are angles
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right now the beautiful things about
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triangle is this the sum of the three
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angles in a triangle is equal to what
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180 180° any triangle that you're going
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to meet any given triangle if you add
1:29
all three angles in the triangles you're
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always going to get what 180 no matter
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what right so matter what the triangle
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looks like the sum of the three
1:38
triangles the three angles are always
1:40
going to be 180 is it just 180 if it's
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an isoses triangle it doesn't matter
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isocles equilateral
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um right triangle the sum of the three
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angles of the triangles are always going
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to be what
1:54
so square would be 360 excuse me would
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it be 360 with a square no square no not
2:00
necessarily if a square will be 360 yes
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why because it's 90 909 90 right a
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square is always going to be 360 a
2:08
rectangle is also going to be what 360
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because each form what a 90° angle
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because you have two parallel lines two
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parallel lines so that's Yeah that is
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true actually so the sum of the three
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angles in the triangle is always going
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to be 180 right now why do we use this
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example if I give you this triangle here
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right i have the measure of this angle i
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have the measure of this angle now I
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want to find this angle what do I do how
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do I find X
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how can I use that right there to
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find subtract the sum of the two from
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180 right because we know that by
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definition x right +
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89 right + 54 is going to be equal to
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what
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180 right so therefore to find x we just
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need to take away take away these two
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angles from it right so x is going to be
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equals to what
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180 -
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89 - 54 and that should give you the
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measure of the third angle X that we're
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looking for right now I'll let you do
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that you know I have to do yours in
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subtraction what you get 27 27 so X is
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27° right and if you add all three
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together if you do 27 + 54 + 39 you
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should get uh 37 37
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okay i'm trusting you guys i'm trusting
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your algebra right we know how to do
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this right so if you do 37 + 54 + 89 you
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should get what 180 if you don't get
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that you get something less or more than
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180 you know that you did something
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wrong okay so this is how you find the
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measure of the third angle if you're
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given uh two angles now let's try this
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problem here i want to see if you guys
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can figure it out right now this is the
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word problem now he's telling us that
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the measures of the angles of the
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triangle ABC are in the ratio 138 what
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are the measures of the
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angles we have an we have a triangle ABC
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and all we know is that there's a ratio
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in between them right we have a
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ratio 1 to 3 to 8 what are the measures
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of the angle how how do you think you
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going to solve this yeah would you put
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like one on A three on B and eight on C
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okay you could do that to start with
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right you could put you can say this is
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the ratio one three and eight then what
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does that mean though
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that means nothing really right now all
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we know is that's a ratio right so how
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do we use this ratio again here so
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you're going to have to like multiply
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them in certain ways to have like one
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and it's going to be one power no it
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would be one three times okay good
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you're getting there all right so now
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when we have something that we don't
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know what letter do we use usually if
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you don't know something X right so
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let's say measure of A was X what do you
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think measure of B is going to be one
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now what's the ratio if one of them is
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one the ratio is what
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3 what 3 X and this is going to be X 8 X
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now can we find now the measure of these
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angles yes because we know that the
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measure of this plus this plus this is
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equal to what
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180 180 so it's going to be 1 x right +
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3x + 8 x is 180 now we can solve for x
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and once we find x we can find the
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measures of any angle right so it's
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going to be
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12x right if you add all these together
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you get 12x is
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180 and then to find x you divide by
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what 12 so what what's 180 over 12
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i can't divide i lost my calculator
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this is bad we can't do some division
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without a calculator
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the problem was 1 12 is equal to what
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somebody else nine is it nine or
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something i can't believe I'm going to
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do myself yes do it yourself
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10us 10 is 120 okay wait is it is it
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like 130
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180id 12 okay so we are sitting here
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thinking about 15 no it's not that 15
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what's 14 15 she has a calculator 15 all
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right 15 even if there was no calculator
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all right so x is 15 or 15 so
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x was right right so x is 15 right so
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that means b is going to be what 45 45
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because we do 3 * 15 right
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that's 45 and then this is going to be 8
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* 15 which is
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120 right yeah totally so this is 120
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all right and if you add them all
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together you're going to get
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what 180 right so this is how you do
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these problems you're given a ratio you
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can use that ratio to find all angles
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because the ratio means there's a
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relationship between the three one of
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them is one if one of them is x the
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other one is 3x and the other one is 8x
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you can solve it right now we're going
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to talk about classifying triangles
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right classifying triangles okay so
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before we do that though we're going to
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talk about um um certain types of angles
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here let me show you
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so we have four different type right
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we have four different type
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all right so
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this is going to be called Lee just
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mentioned what is it
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acute angle right acute angle why do we
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call it an acute angle because it's less
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than 90° it's less than 90° is less than
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90° right less than 90° the measure of
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the angle is less than 90° now this is
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what I mean right angle that is 90
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because it's exactly what 90° right
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right angle
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and then this is a triangle of this
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triangle up because of what it's big
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it's more than what it's bigger than 90°
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more than 90° up more than 90 right it's
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90° and then this is basically the a
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line a straight angle right or a flat
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because the whole thing is what 360 No
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180 right so this is a flat or straight
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angle straight angle straight angle
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because the measure
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is
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80° all right so
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uh this is pretty much and then if you
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Oh no we we have like if you look in
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your book we don't have to like I don't
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have to put it on put this on the board
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okay if you look at triangles and if you
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find that all the measure all the
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measures of the angles in the triangles
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are less than is less than like 90 is
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going to be a acute triangle right and
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if you have uh an angle in a triangle
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where one of the angles is more than 90
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is going to be the obus and then the
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last one is going to be a right angle
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right triangle because we know that you
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have the hypotenuse we have two legs
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they form a 90° so that's a right angle
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okay and you also have some minor ones
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you have a scaline triangle because no
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congruent sides and you have the
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isoclesles triangle because two sides
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are what
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isocles
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triangle are the same and then one is
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different and then the last one is a
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equilateral triangle which is all three
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sides are the same okay so this is
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basically this type this section this is
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pretty simple stuff so we should just
10:15
munch on it i give you homework now we
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can start working on it right now all
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right a very very easy section not that
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hard everybody was
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