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In the figure shown, WV + VU = 10,VU = 5, and TV WU. Prove ATVW = ATVU:W...

Question

In the figure shown, WV + VU = 10,VU = 5, and TV WU. Prove ATVW = ATVU:W

In the figure shown, WV + VU = 10,VU = 5, and TV WU. Prove ATVW = ATVU: W



Answers

Show that $T U V W$ is a parallelogram for for $a=19.5$ and $b=22$ (FIGURE CANT COPY)

Question number four. Yeah. On their day off this is X. As the. Uh huh. It has given that D. N. A. Tricycle established access and X. W. Water congress Angeles mangled to concord creature. I don't want to each other not to physically go there. XD and excess. I'm going teacher. So that district went home visit so fast. Is that two? Uh huh. Crazy has doubled Christine. Who just try sipping and say that testing is congruent to. I don't know. All right. It is there that I'm going to talk to you post just respecting all Puerto rico. Yeah. Thanksgiving with us. Do you know tricep his government? Right? So number three. This given that access Yes I'm going to that stuff. You know this group. Uh huh. Well in that angle s this can go to hungry. I don't know the girls living. And I can see. And triangle X. S. D. And X. R. W. Two side said hunger to each other and corresponding angle also when under the immigration. And the words come so you can see that triangle X. Sp is I'm going to the triangle. Let's end up what is really going to Polo asked. It is so it is cool. Mhm. Well now the anger Sanders our Congress, the corresponding sides household congo. So you can write access when we can go to next up. Let's see what so like the bones of both secrecy. Yes sir, corresponding parts of congruent triangles are also Congress hands access. That's not acceptable room. Thank you.

I We're looking at Question 21 which is a proof. And so I'm setting up my two columns here. You can do it in two column format or whatever format you've been using in class. And keep in mind that are. Diagram is for several different questions, and diagrams aren't always drawn to scale. So, um, we want to go. If something. If we're told something's congressional, we're going to know that it's convert, even if it doesn't look like it in the picture. And there's a couple of ways of doing proof. Some people like to do all the statements and then all the reasons some people doing together today I'm gonna do all the statements and then fill in all the reasons and our first statement is always are given. So PS equals R Q. And then peak, you equals Rs. And the first thing that we're gonna want to do here is convert those to congregants. Um, some teachers I know don't make you do this, but this is the more formal method of doing proof because our therms actually say that we have to have congruent sides not equal sides, so we can change PS can grow into our cue. And that would be definition of concurrence or equal measures give concurrent segments and then the same thing. We can do it on the same line because we have the same reason for both. So P Q is concurrent toe R s and now we need to prove are trying. Those converts were trying to prove our lines parallel, so we need to get some corresponding angles. Congrats. And since our triangles share the side qs, we can say that Q s is concurrent took us by the reflexive property, which then allows us to say that are triangles are congrats. Because if you notice I have two sets, asides here and then a set asides here so I can prove my triangles concurrent by side, side side. So I'll say Triangle Peak us is congratulated, too. Triangle R S Q. And then I can get my corresponding angles. Congregant, be careful which set of angles you pick because we need to prove pique is peril to rs. So we need the alternate interior angles that would go with P Q and R s, which is angled to an angle three. If we use dangles one and four, we would be able to say that P S and R Q are parallel, but that's not what they asked us for. Make that a six. Um So then we can say that peak you is parallel to rs. So now I'm going to go through and put my reasons in. Oops, There we go. So my first is given. And then my second, If you recall we talked about you can either say definition of congruence or equal measures or equal links, give congruent segments and then reflexive property congruence which retired. And then we know that triangles air congrats by side, side, side and then we is the corresponding heart. Parts are congruent, triangles can grow int. And then finally, two lines with trans versatile an alternate interior angles grew ins, give parallel lines or something like that.

Given T. W. Is a median and S. T equals X plus 40 S W equals two. X plus 30 and W V equals five X minus six. We're going to determine the length of the segments. Sw W. V. And S. T. I've already labeled the diagram here for each of those segments. And the first thing we're going to say is that S. W equals W. V. This is because we are told that tw here is a median, which means that it cuts S. V. And the two congruent segments, so S. W. And W. V are equal to one another. Now we can use substitution SWS two X plus 30 Equals WV. Which is five X -6. I'm going to subtract 2x. From both sides. We get 30 equals three X -6, Add 6 to both sides. We get 36 equals three. X Divide both sides by three And we get 12 equals x. Now that I know how big X is, we can determine how long each of these are. Yeah S. T. is x plus 40. So s. t. equals 12 plus 40. S. T. is 52 units. Sw is two X plus 30. So sw is two times 12 plus 30. S W equals two times 12 is 24 plus 30 24 plus 30 is 54. And lastly we have W. V. Which is five X -6. So five x -6. WV equals five times 12 minus six. WV equals 60 -6. WV equals 54. And we noticed that W. V. And S W. Here are the same and that makes sense. Since we were able to say S. W equals W. V over here, they are congruent. Therefore they should be the same value. The fact that they are means that we did things correctly. So S. T. Is 52 units. And S W N W V. R 54 units.

For a problem to We are given a triangle with a line running through it, um, and were given some specific measurements. And we need to find segment p que the length of segment peak you So that segment would be here. So we're finding this whole side of the triangle here. So first, we're gonna label what we know and then try to find out what we need to find out. So first they gave us. The PS is equal to 53.3. So frumpy toe s, that is 53 point four units long Q t from Q T is 47.7 units on what he said on 0.7 and then from cute esus 53.4 right here. So remember, we're supposed to be finding how long P Q is. Well, we know what from que tu t is, but we don't know what PTO t the length of PTT is. So we can't find out peak you until we know Petey. So let's look at what we do know. Well, I see right now two very important things. First I see that PS and QS Arkan grew it because they both equal 53.4. So I'm gonna label that on my figure. I also see that the line em cuts the segment P Q at a right angle. So I'm gonna go ahead and write down what I know. First, I know PS is equal to Qs. I also know that line em because it hits cute pic you at a right angle that makes it perpendicular to the segment peak you because when it creates that writing is perpendicular So knowing these two things I can think of a the're, um, I can use to help me figure out the segment P. Q. What fear, Um, is it It's the converse of the perpendicular by sector. The're, um this their, um says that if you have two sides that are equal, which we do on a line that is perpendicular to a segment, then we know that the segment the line is cutting the segment with a perpendicular by sector. So that means that p que is being bisected by the line em. So that means PT is congruent to t. Q. I'm giving them to take Mark's because they're not the same as 53.4, so it's different, but they are concurrent to each other. So if Q T is 47.7 units long, then that means that Petey is as well because they are perpendicular. Lee bisected. So now that I know what PT is, I can find the whole p que by adding 47.7 to itself or multiplying it by two. And when I do that, I get 95.4. So by using the converse of the perpendicular by sector theorem, we found that P Q is 95.4 units long.


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