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TommyTrojan
Nick plotted A(2, 2), B(3, 4), and C(4, 2) and joined the points to form triangle ABC. He plotted two other points at P(-3, 4) and Q(-2, 2). What should be the coordinates of the third point R to form triangle PQR that is congruent to triangle ABC? (-1, 4) (-2, -5) (-5, 2) (-4, 1)
@KonradZuse @AccessDenied
Have you tried plotting the points that you were given?
Yes, but I still don't get it
Could you post that graph here? :)
I actually wrote it on loose leaf paper lol. Soz
But how would you do it?
My first step is graphing the points. Then, I'd look for any obvious solutions like if there were symmetries between the points...
OK can I ask you a few more?
Oh, I just realised something -- the points have to correspond for the congruence! It's been a bit since I've done Geometry... lol. :P Let me graph it myself quick.
OK thank you lol no problem
PQ = AB QR = BC PR = AC
So it is either a or b
We could either do something like guess and check each point to see if it is the same, or maybe use some algebra and find the point which is a distance of BC from Q and a distance of AC from P
I got a. Is that right?
A) appears correct to me as well. :) For Geometry, if it weren't so obvious, we could use distance formula for some arbitrary point R(x,y) that meets those two distance conditions and solve that two-variable system. This one is pretty simple to "see" though.
I have a few more questions, if that's all right with you?
I think we'd get two solutions, one would be some sort of fraction or rational and (-1,4) also.
Sure, that's fine. :)
OK thank you so much Triangle PQR is similar to triangle ABC in the figure below. What is the perimeter of triangle ABC? 10.5 inches 39.9 inches 42.0 inches 60.65 inches
I got B, just checking my work.
How did you get B)?
Tell you the truth, I guessed, i'm confused on how to do it.
Ah, okay. Well, we'd like to first find that one side length that we don't know on the triangle. Ratios of corresponding sides on similar triangles have to be the same, so this is one way to approach it. Set up this proportion of the sides: \( \displaystyle \frac{\text{AC}}{\text{PR}} = \frac{\text{AB}}{\text{PQ}} \) Notice how these are in fact corresponding sides; we can tell by which angles they are between, or just by position in the name of the triangles. \( \color{green}{\textbf{A}}\text{B}\color{green}{\textbf{C}} ~ \color{green}{\textbf{P}}\text{Q}\color{green}{\textbf{R}} \)
So, can you find the length of that side (AC) given this information?
Correct. :) Now, we just sum the lengths of the sides.
Your VERY helpful, but I have alot more questions if that's all right with you. PS i'll medal you when we're all done, or now if you want.
Hmm, how many questions? :)
Most of them are just checking though
Ok let's get started then lol. Jeremiah uses bamboo rods to make the frame of a tailless kite. He ties three bamboo rods together to form a right triangle PQR. He then ties another rod from P that meets RQ at a right angle. Segment PS in the figure below represents this rod and it is 4 inches long. Which of the following could be the lengths of segments QS and SR? QS = 2 inches, SR = 8 inches QS = 6 inches, SR = 10 inches QS = 2 inches, SR = 2 inches QS = 4 inches, SR = 12 inches
I got A. Is that correct?
If I recall this type of situation correctly: PS/ QS = RS/ PS 4 / QS = RS / 4 A) 4/2 = 8/4 ==> 2 = 2. Appears to be correct. :)
OK An architect planned to construct two similar stone pyramid structures in a park. The figure below shows the front view of the pyramids in her plan but there is an error in the dimensions. Which of the following changes should she make to the dimensions to correct her error? change the length of side AB to 2 feet change the length of side PQ to 8 feet change the length of side AB to 1 feet change the length of side PQ to 4 feet
Hmm, do you have an answer to check?
No this one I don't quite understand.
Ah, okay. This is another similar figures question. The key here is having the same side ratios again, similar to some earlier problems. First, I'd check each side ratio to see if there is a sort of "odd-man out."
Our corresponding sides: AC ~ PR, AB ~ PQ, BC ~ QR We should check all three of these ratios. AC/PR, AB/PQ, BC/QR
Ok i plugged in the numbers but now what?
What do you get for each ratio? Is one of them different?
AB-PQ is the different on it gets 1/2, while all the other ratios get .3 repeated
Yep. So, we'd like to find the solution that changes AB or PQ to match the other two side ratios.
For this, we could just go through each proposed solution and check to see if it works out.
Ok only 2 more left.
Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 1.8 inches and the length of segment CR is 3.3inches. The distance between A and C is 6.6 inches. What is the distance between the endpoints of the beams P and Q? 3.6 inches 0.9 inches 1.8 inches 2.5 inches
Here is another case of similar triangles. Can you identify the side-ratios here? Just to see if you understand the similar triangles have side ratios detail. :)
Oh I forgot to trell you I got A.
Ah, okay. A) is correct to me. :) We set up a simple side ratio: QR/PR = AC/PQ' 3.3/1.8 = 6.6/x; x = 6.6 * 1.8 / 3.3 = 3.6
Moris drew two triangles; triangle ABC and triangle PQR, on a coordinate grid. The coordinates of the vertices of triangle PQR are P(-3, -2), Q(-3, -4), and R(-1, -4). The coordinates of the vertices of triangle ABC are A(-3, 4), B(-1, 4), C(-3, 2). Which postulate can be used to prove that the two triangles are congruent? SAS, because AAA, because ASA, because SSS, because
Yeah, I am thinking D) as well. We're given all the points, we could easily just take distance formula or if they're horixontal/vertical, count.
Well I guess that's it, I have more but, since I only said 5 I will keep my word and let you go. OK Thanks though
You're welcome! :)