module 4 lesson 2 remediation. parallel lines lines that are coplanar and never intersect....
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Module 4 Lesson 2 Remediation
Parallel Lines
• Lines that are coplanar and NEVER intersect.– Remember that COPLANAR means on the same plane
H
F
G
E
D C
BA AE, DH, CG, BF would all be parallel to each other.
AB, DC, HG, EF would all be parallel to each other.
AD, BC, FG, EH would all be parallel to each other.
Skew Lines
• Lines that are NON-coplanar that NEVER intersect.– Remember that NON-coplanar means not on the same plane.
H
F
G
E
D C
BA
DC and GF would be skew lines.
AE and HG would be skew lines.
Examples1. Name a line parallel to ZT.
2. Name two parallel lines.
3. Name a line skew to RX.
4. Name two skew lines.
U
S
T
R
Y Z
WX
1. Sets of parallel lines
XY, WZ, ST, RU or WX, ZY, UT, SR
2. Sets of skew lines
YU, WZ WS, YZ ZT, YX YX, UT
YU, ST WS, UT ZT, UR YX, RS
YU, WX WS, YX ZT, RS WX, ST
YU, SR WS, UR ZT, WX WX, RU
ST, XR TU, XR XW, RU WZ, XRZY, XR XW, ST
WZ, UT ZY, RU YX, UT XW, RU
WZ, RS ZY, ST YX, RS XW, ST
AnglesAlternate Exterior (Congruent) Alternate Interior (Congruent)
AnglesCorresponding (Congruent) Consecutive Interior
(Supplementary)
ExamplesFind the missing angle.
1.)
2.)
Alternate Exterior Angles? = 65°
Consecutive Interior Angles? + 96 = 180 - 96 - 96? = 84°
Examples
Find x.
3.)
4.)
Consecutive Interior7x + 14 + 12x + 14 = 18019x + 28 = 180 - 28 - 2819x = 15219 19x = 8
Corresponding120 = 10x + 10- 10 - 10110 = 10x 10 10x = 11
You try...1.) 2.)
3.) 4.)
3.) consecutive interior14x + 5 + 44x + 1 = 18058x + 6 = 180 - 6 - 658x = 174 58 58x = 3
2.) corresponding? = 100
1.) consecutive interior? + 102 = 180 - 102 - 102? = 78
4.) alternate exterior12 + 4x = 6x – 12 - 4x - 4x12 = 2x – 12
+ 12 + 12 24 = 2x
2 212 = xx = 12