This design was made by wrapping string around nails. Triangle KLP is congruent to triangle MLP. Which of the following statements is false?

The length of segment JP = 9 in.
The measure of angle LKJ = 46°.
Segment LP bisects angle JPN.
The measure of angle KLJ = 44º.

Question

This design was made by wrapping string around nails. Triangle KLP is congruent to triangle MLP. Which of the following statements is false?



The length of segment JP = 9 in.
The measure of angle LKJ = 46°.
Segment LP bisects angle JPN.
The measure of angle KLJ = 44º.

campayne · Answer

attachment

thatonegirl_ · Answer

Which do you think it is?

campayne · Answer

i haven't the slightest clue

thatonegirl_ · Answer

Okay well we can test each one. How would you find the length of JP?

campayne · Answer

umm use the other congruent triangle, right?

thatonegirl_ · Answer

Well, an easier way would be to use the Pythagorean theorem. Are you familiar with it?

campayne · Answer

indeed i am

thatonegirl_ · Answer

Okay great :D So try to use it to find JP.|dw:1469567512372:dw|

campayne · Answer

10.29?

thatonegirl_ · Answer

What was your work for that?

campayne · Answer

well 5 squared is 25 plus 9 squared 81 equals 106, and the square root of that is 10.29

thatonegirl_ · Answer

Ah, don't forget that c^2 is always the hypotenuse. So your equation should look like $$5^2+b^2=9^2$$

campayne · Answer

fudge..

campayne · Answer

so then 7.48

thatonegirl_ · Answer

Lol you're good. And correct!

thatonegirl_ · Answer

So you know that the first one is false then :) I checked the others to make sure they were true and they are. Would you like me to go through those with you so you can check that you have the right answer?

campayne · Answer

yes

thatonegirl_ · Answer

Okay so what do you know about angle measures and congruent shapes?

campayne · Answer

umm some

thatonegirl_ · Answer

Well the angle measures are always the same. For example: |dw:1469568320506:dw|

thatonegirl_ · Answer

the "???" would also be 45° if the triangles are congruent

thatonegirl_ · Answer

Sorry i mean to type a 4 for that other side.. But you get the idea. So back to your triangles, were told that the 2 on the outside are congruent.

campayne · Answer

i see

thatonegirl_ · Answer

So you know that the 2nd one is true :)

campayne · Answer

indeed

thatonegirl_ · Answer

Do you know what a bisector is?

campayne · Answer

umm. cuts something in half?

thatonegirl_ · Answer

Yup pretty much. So would you say that segment LP cuts that angle in half?

campayne · Answer

yes i would

thatonegirl_ · Answer

Okay so then that one is true too. Last one, subtract 180 (the entire triangle) by 90 (since it's a right triangle) and 46 (which we established was that other angle). You get 44, so the last one is also true.