• shyguy10918
They are vertically opposite angles. Similarly, you can show that angle LNM and angle MKJ are also vertically opposite angles. Now, look at the angles MKJ and KJL. They are alternate interior angles and are equal because lines KL and UE are parallel (since they are bisectors of each other). Similarly, you can show that angles LNM and LME are equal. Thus, you have two pairs of congruent angles and a side, KL, that is common to both triangles. Hence, by ASA (angle-side-angle) congruence rule, triangles MNL and JMK are congruent. This means that line EN is congruent to line JU since they are corresponding sides of congruent triangles. Therefore

## Homework Statement

E 1\---------------------------------1N
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
K 1---------\-M---------------------1L
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
1 \ 1
J 1---------------------------------\1U
K is the midpoint of line JE
L is the midpoint of line UN
line KL and line UE bisect each other at point M
Prove:JUNE i a parallelogram

## The Attempt at a Solution

statement 1 reason
--------------------------------------------------
1)K is the midpoint of line 1 1) given
JE 1
2)line KE is congruent to 1 2) midpoint is the center of a line segment
line KJ 1
3)L is the midpoint of line 1 3) given
UN 1
4)line NL is congruent to line 1 4) midpoint is the center of a line segment
LU 1
5)line KL and line UE bisect 1 5) given
each other at M 1
6)line EM is congruent to line 1 6) line bisector splits the line segment in half
MU 1
7)line KM is congruent to line 1 7) line bisector splits the line segment in half
ML 1
8)triangle EKM is congruent to1 8) theorem of Side,Side,Side
triangle ULM 1
9)line EK is congruent to line 1 9)corresponding parts of congruent triangles and congruent
UL 1
10)line KJ is congruent to line 1 10)substitution
NL 1
11)line EJ is congruent to line 1 11)substitution
NU 1
This is where i am stuck,how can I prove that either line EN is congruent to line JU or that line EJ is parallel to line NU?

for some reason the picture isn't coming out on this part. it is suppose to be a diagnol EU and a line NU.

Why is this a "calculus and beyond" question? Looks like basic geometry to me.

Also I don't see any indication of what YOU have done. If we don't know what kind of help you need, we can't give you any help.

sorry for wrong area. all the work i did is at the bottom same with what i need help with

You need to prove that triangle MNL is congruent to triangle JMK. Look at the angles NLM and JKM.