WEBVTT 1 00:00:00.768 --> 00:00:02.560 Welcome to Brainfuse! 2 00:00:06.400 --> 00:00:12.544 In this lesson, we're going to classify each triangle on screen by its sides and angles 3 00:00:12.800 --> 00:00:15.104 These terms are important to remember 4 00:00:15.616 --> 00:00:18.432 And use when you're working with triangles. 5 00:00:18.688 --> 00:00:24.832 So we'll start with the sides; I'll write anything that has to do with sides in blue and 6 00:00:25.088 --> 00:00:28.160 Then angles, we will put in purple. 7 00:00:30.208 --> 00:00:34.560 So our first triangle we will work with is this green triangle 8 00:00:35.328 --> 00:00:41.472 Notice it doesn't give us the measures of its sides or its angles, but it does give us one clue about its measurements 9 00:00:41.984 --> 00:00:48.128 It includes these tick marks and these tell us that every side with this tick mark in one triangle 10 00:00:48.384 --> 00:00:52.480 is going to be equal. As a result I know it has 11 00:00:52.736 --> 00:00:59.136 Three equal sides 12 00:00:59.136 --> 00:01:03.824 And that makes it equilateral. 13 00:01:08.864 --> 00:01:12.192 These tick marks actually tell us about the angles as well. 14 00:01:12.448 --> 00:01:12.448 15 00:01:12.448 --> 00:01:16.032 In order for these sides to be of equal length 16 00:01:16.544 --> 00:01:19.360 The angles need to be equal as well. 17 00:01:21.920 --> 00:01:22.982 If that's the case, 18 00:01:22.982 --> 00:01:26.272 If I make this x degrees, 19 00:01:26.784 --> 00:01:28.064 Then we know that 20 00:01:28.320 --> 00:01:31.392 The other angles can have the same variable 21 00:01:31.648 --> 00:01:33.696 Because they're all the same value. 22 00:01:34.720 --> 00:01:37.792 If we find the sum of all three angles, that sum 23 00:01:38.048 --> 00:01:43.139 Always equals 180 degrees for a triangle. 24 00:01:43.139 --> 00:01:49.824 So we have x + x + x = 180. We combine like terms 25 00:01:50.336 --> 00:01:53.664 And that's 3x = 180. 26 00:01:54.176 --> 00:01:59.808 Divide both sides by 3 and we find that x is equal to 60 degrees. 27 00:02:00.320 --> 00:02:00.320 28 00:02:00.320 --> 00:02:04.928 So, if you think about angles, is 60 degrees a right angle, 29 00:02:07.232 --> 00:02:08.768 An acute angle, 30 00:02:09.792 --> 00:02:11.584 Or an obtuse angle? 31 00:02:13.376 --> 00:02:17.472 60 degrees is less than 90 degrees 32 00:02:17.728 --> 00:02:19.776 And that makes 33 00:02:19.776 --> 00:02:19.776 34 00:02:20.032 --> 00:02:24.640 An acute angle. So if all three angles are acute 35 00:02:27.968 --> 00:02:30.999 We then have an acute triangle. 36 00:02:31.552 --> 00:02:37.696 Since we probably won't have room to keep writing "triangle" on screen I'll just use this 37 00:02:37.696 --> 00:02:40.000 Shape as a symbol. 38 00:02:46.912 --> 00:02:47.424 39 00:02:47.680 --> 00:02:51.008 So now let's move on to the purple triangle. 40 00:02:51.520 --> 00:02:52.800 And here 41 00:02:53.056 --> 00:02:55.616 We see two tick marks instead of three, 42 00:02:56.128 --> 00:02:59.200 So that tells us that it has two equal sides, 43 00:03:03.552 --> 00:03:10.066 And a triangle with two equal sides is called an isosceles triangle. 44 00:03:12.000 --> 00:03:13.536 Now what about the angles? 45 00:03:14.048 --> 00:03:17.888 Here we are given one angle. We're told that this is 50 degrees 46 00:03:18.400 --> 00:03:20.448 So if the line on the right 47 00:03:20.448 --> 00:03:25.892 Is equal to the line on the left, that means the angle opposite the line on the left 48 00:03:25.892 --> 00:03:27.360 Also needs to be 49 00:03:27.616 --> 00:03:29.408 50 degrees. 50 00:03:29.664 --> 00:03:31.968 Now we just add up 51 00:03:32.224 --> 00:03:34.528 What we know so far. 52 00:03:36.064 --> 00:03:36.576 53 00:03:38.368 --> 00:03:38.368 54 00:03:38.368 --> 00:03:46.048 50 degrees + 50 degrees is equal to 100 55 00:03:46.048 --> 00:03:49.632 And we subtract that total from 180 56 00:03:49.888 --> 00:03:54.496 To find that the measure of this angle 57 00:03:55.008 --> 00:03:57.312 Would be 80 degrees 58 00:03:57.568 --> 00:04:03.712 Are all of those angles under 90 degrees? If they are, then this is also an 59 00:04:03.968 --> 00:04:05.248 An acute triangle 60 00:04:07.296 --> 00:04:08.576 And note that 61 00:04:09.088 --> 00:04:13.184 Not all isosceles triangles need to be acute 62 00:04:13.696 --> 00:04:17.536 So make sure you pay attention to the measurements of each angle. 63 00:04:28.544 --> 00:04:31.360 Next we have the red triangle, 64 00:04:31.616 --> 00:04:32.640 And 65 00:04:32.896 --> 00:04:36.480 We don't see any tick marks so there aren't any clues 66 00:04:36.736 --> 00:04:42.880 That tell us that its sides are equal and as a result we're going to say 67 00:04:43.136 --> 00:04:46.720 It has 0 equal sides, 68 00:04:47.488 --> 00:04:50.304 And that makes it a scalene triangle. 69 00:04:54.400 --> 00:04:57.472 And moving to angles, what do we know about the angles? 70 00:04:57.984 --> 00:05:02.080 We have one measurement here that is 120 degrees, 71 00:05:02.336 --> 00:05:04.128 So that gives us one 72 00:05:04.384 --> 00:05:10.528 Obtuse angle because 120 is greater than 90 degrees. 73 00:05:12.064 --> 00:05:19.232 So if a triangle has one obtuse angle, it is considered an obtuse triangle. 74 00:05:19.232 --> 00:05:19.232 75 00:05:24.608 --> 00:05:24.608 76 00:05:25.247 --> 00:05:29.984 Finally, we have our light blue triangle and 77 00:05:30.240 --> 00:05:34.592 Let's see what we know about the lengths of its sides 78 00:05:34.848 --> 00:05:37.920 In terms of clues, we don't have any tick marks 79 00:05:38.176 --> 00:05:41.530 But we do have this symbol, 80 00:05:41.530 --> 00:05:47.392 Which tells us this is 90 degrees, so it's a right angle. 81 00:05:47.648 --> 00:05:52.512 And if we know this is 45 degrees, let's subtract 82 00:05:52.768 --> 00:05:58.400 180 - ( 90 + 45 ) 83 00:05:58.400 --> 00:05:58.400 84 00:05:59.424 --> 00:06:05.568 90 degrees + 45 degrees is equal to 135 degrees 85 00:06:05.824 --> 00:06:12.224 And 180° - 135° leaves us with 45 degrees. 86 00:06:12.224 --> 00:06:14.016 87 00:06:15.552 --> 00:06:19.624 We know that there are many kinds of right triangles, this happens to be a 88 00:06:19.624 --> 00:06:23.744 45-45-90 triangle, 89 00:06:28.352 --> 00:06:31.936 So we know that the sides opposite these equal angles 90 00:06:32.192 --> 00:06:34.496 Also have to be equal. 91 00:06:36.288 --> 00:06:39.104 So the legs would be equal. 92 00:06:39.360 --> 00:06:44.480 As a result we know that this particular right triangle is isosceles 93 00:06:44.736 --> 00:06:46.272 Because it has two 94 00:06:46.528 --> 00:06:51.392 Equal sides. 95 00:06:51.392 --> 00:06:52.928 I will write it up here so it's clear 96 00:06:58.816 --> 00:07:04.960 Finally, in terms of angles, we know that this has that 90 degree angle so that makes it 97 00:07:04.960 --> 00:07:06.496 A right triangle. 98 00:07:06.752 --> 00:07:19.040 One 90 degree angle makes it right. 99 00:07:20.805 --> 00:07:25.662 You can now click on "Live Help" to work with a tutor on solving problems 100 00:07:25.662 --> 00:07:30.737 With each type of triangle we've reviewed. And thank you for watching this lesson.