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01:05

Suzanne W.

In Exercises $5-11$ you will have to visualize certain lines and planes not shown in the diagram of the box. When you name a plane, name it by using four points, no three of which are collinear. Write the postulate that assures you that $\overrightarrow{A C}$ exists.

00:39

Evan S.

Classify each statement as true or false. $A, B, C,$ and $D$ are coplanar.

00:18

Classify each statement as true or false. $h$ is in $R$.

00:07

Amrita B.

State Theorem $1-2$ using the phrase one and only one.

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Hey, guys, Mr Kleinberg here with some equilateral and isosceles practice problems. So here we have an isosceles triangle. What that means is you have two sides that are equal, and you can see that by both of them being labeled for and four. So I wouldn't have to put those tick marks to indicate that, but just reaffirming how to use the symbols, what they mean and that sort of thing, or that this angle here is called the Vertex angle. At the bottom side. That's not one of the congruent sides is known as the base, and that the two angles at the bottom are known as face angles and they're equal or congruent. So what that means if we're going to solve for X on, why, here's what I do know. I know that X has to equal 66 degrees because the two bass angles are congruent now if I know that both of them are 66 degrees in the sum of the angles in a triangle is 180 what I can do is I can subtract 66 66 from 1 80 that results and a Y value of 48 degrees. So that would be one way we can solve the triangle, knowing the properties of an isosceles triangle. If we look at an equilateral triangle, remember any collateral triangle also known as an equal, angular triangle, also known as a regular triangle? And this is a word that might pop up later. The fact that it's regular means all sides and all angles are equal, meaning all sides we call to each other, and all angles are equal to each other, respectively. So the fact that this is an equilateral triangle means every angle 60 degrees that's gonna force to white and equal 60. Or, in other words, y equals 30 and also forces the two sides here three X plus eight to be equal to four x minus four. Okay, well, that's gonna get us 12, equals X. So if I wanted to then figure out what the actual site links are, I could plug 12 in four times 12 was 48 minus four ISS 44. So the length of this site would be 44 and you can verify that if you plug it into here. Three times 12 is 36 plus an eight is also 44 which is consistent with the value we found a couple other questions that you might see would be all right. Let's suppose I have unequal or apartment isosceles triangle, and I know that the Vertex angle is 40. What is then the base angles? What are they worth, or what is their value? Well, if we know that the Vertex angle is 1 41 80 which is the sum of all the angles in a triangle minus 4140. But because these two are equal, then it's like saying to X equals 1 40 or in other words, each of them is equal to 70 degrees. In this next example, we have an equal lateral triangle, and we know that the perimeter is 16. Well, what is X, then? Well, think about it. If all the sides are equal, then three X plus threes would have to equal 16. That would be three. X plus nine equals 16. Well, that would be three X equals seven. Or, in other words, X equals seven thirds. And now, if you wanted to figure out what the actual length was, we could plug seven thirds in way could figure that out. But this is just a few. A couple of problems you might see given. And I saw slaves or unequal lateral triangle. I'll see you next time.

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