Question

Triangle LMN is similar to triangle QRS. Using the image below, prove that parallel lines have the same slope.

Answer 1

Sorry, not sure how to prove it. :3

Answer 2

I would start by saying:
extend line segment MN so it connects to point R, and forms
line segment MS, a transversal crossing lines LM and QR


because the triangles are similar the corresponding angles <LMN = <QRS

because these angles are corresponding angles of the transversal, we know line
LM is parallel to line QR

now find the slope of line LM and the slope of QR

Answer 3

@mathmale could you explain this a bit more for me. i'm still confused by it

Answer 4

Let me turn this around a bit and ask you to pose questions regarding what you don't know or what you believe you need to know to solve this problem.

Answer 5

ok. well would i use y2-y1/x2-x1 to get the slope of the different lines?

Answer 6

@mathmale

Answer 7

Certainly that would work, if you had numerical measurements to work with. But what if you don't have such measurements? In that case you'd have to operate with the information given.

One of the basic principles we learn in algebra, early, is tht two lines with that are parallel have the same slope. Could you use that fact in your proof?

Answer 8

yes. but i also have to show work. the graph shows the numbers for the points so could i use those numbers with the smaller triangle and get the slope using them then use the fact to explain why?

Answer 9

@mathmale

Answer 10

You have 2 triangles. Assuming that you're able to find all 3 sides of each triangle, based upon the fact that the triangles are similar, then you could certainly apply the slope formula to show that the two slopes in question are equal.

Answer 11

so using the y2-y1/x2-x1 formula if i got the cord points and imputted them into the formula i would be able to get the slopes of all 3 sides from it?

Answer 12

Was there, by any chance, an illustration that came with this problem? if so, would you please share it? Perhaps you could do a screen shot and upload the image here.

Answer 13

it is at the top of the question

Answer 14

No, not the slopes of all three sides (although it wouldn't hurt to find all 3 slopes pertaining to each triangle and then to compare them). Showing that any 2 parallel lines (1 in one triangle and 1 in the other triangle) have the same slope would be entirely sufficient.

Answer 15

Sorry. didn't see the illustration. The illustration makes this problem so much simpler.

Answer 16

heres the image again. so i just have to find the slope of one side (the same one) but one different triangles

Answer 17

on different**

Answer 18

To answer that: please have another look at the illustration. Can you identify the hypotenuse in each triangle? If the two triangles are similar (which the problem says they are), then the two hypotenuses are parallel. Believe that?

Answer 19

If you do, find the slopes of the two different hypotenuses separately and then compare your results.

Answer 20

ok thank you :) i understand what to do now.

Answer 21

I'm glad! See you again soon!