CAHSEE practice: Problems 38-42

Problem 38. In the drawing below, the figure formed by the squares with sides that are labeled x, y, and z is a right triangle. So the figure, so it's a right triangle. And then they ask us, which equation is true for all values of x, y, and z? So really, they're just trying to see if you remember the Pythagorean Theorem. And that just tells us that if we have a right triangle, that the sum of the squares of the two smaller sides, so x squared plus y squared, is going to be equal to the square of the longest side, or the side that's opposite the right angle. Or we also call that the hypotenuse. So that's equal to z squared. That's what the Pythagorean Theorem tells us. And so if we look down here, only one of those match what I just wrote down, are kind of my restatement of the Pythagorean Theorem. x squared plus y squared is equal to z squared. And that's this one right there, choice B. Next problem. Problem 39. A clothing company created the following diagram for a vest. So I guess this is somehow a vest. Maybe it's half of the vest, because I don't see how I could put that on me. To show the other side of the vest-- OK, right, so this was half of the vest-- the company will reflect the drawing across the y-axis. What will be the coordinates of C after the reflection? So when they say reflection, they mean, literally, just take the image of this and you flip it over onto the right-hand side. So I could draw it out, and draw it in blue. So if I take the reflection, this line right here is at negative 1. It's 1 to the left of the y-axis. So when I take its reflection, I would draw it right here, 1 to the right of the y-axis. This line down here, it goes from 1 to the left all the way to 4 to the left. On this side, it's going to go from 1 to the right all the way to 4 to the right. I could keep doing it. This segment right here, FE, when I flip it, will become this segment right here. This segment, DE, right here, will become this segment. It'll just look something like this when I go onto that side. And then C, right here, is 2 to the left of the y-axis. So C over here will be 2 to the right of the y-axis. So it's going to look something like this. So the vest is going to look something like this. And then of course, it just dips down like that. So that's the right-hand side of the vest. But they want to know what are the coordinates of C? So this is C, and this is the C after the reflection. Maybe I could call it C prime. And so its coordinates are-- its x-coordinate is 2. And we're 2 to the right; before, we were 2 to the left, at minus 2. And its y-coordinate is going to be the same, it's going to be 7. 2, 7. So that is choice A. I'll do it in the next video. Well, there's only two problems in this video. So let me go to the next page. Number 40. What is the area, in square units, of trapezoid QRST shown below? So we need to figure out the area of this. And they actually even give us a formula. They gave us the formula for this trapezoid. So they're calling it 1/2 times the height, times base 1 plus base 2. So essentially, just to give you an intuition of where this comes from, you're essentially saying, what's the average width of this trapezoid? So you take 1/2 times the sum of this guy and that guy, and that gives you the average width. And then you multiply that times the height. So just applying this formula, it is 1/2 times my height-- my height is 8-- times base 1, let's call this base 1, 20. Plus base 2. Base 2 is this 6 right there. So I have 1/2 times 8, which is 4, times 26. And 4 times 26 is equal to 104 square units. So that's that right there. So they're really just testing whether you can apply this formula. Whether you can recognize what's the height and what are the two bases. Problem 41. One millimeter is. Well, here they're just seeing if you remember your units. Let me write it this way. Deci is equal to 1/10. Centi is equal to 1/100. And then milli is equal to 1/1000. So one millimeter is 1/1000 of a meter. They're just making sure you remember your metric prefixes. Problem 42. In the diagram below, hexagon LMNPQR is congruent to hexagon STUVWX. Congruent just means all the sides are equal and all the measures of their angles are also equal. So they say, which side is the same length as MN? So this is MN right there, and we want to know what side is the same length as that. So let me make sure that they're not trying to confuse us. So they start here, they say LMNPQR, and then they say STUVWX. So they're not confusing us. These points do correspond. S corresponds to L, M corresponds to T, and so forth and so on. So this segment is going to be congruent to that segment right there. Segment TU. So MN is the same length as TU. That is choice B.