Download Math 8 Unit 6 Congruence

Math 8 Unit 6 Congruence
Winter 2007
References
Helpful Links:
http://www.studystack.com/s
tudytable-56459
http://www.mathnstuff.com/
math/spoken/here/2class/26
0/trans.htm
http://www.studyzone.org/m
testprep/math8/g/8parallelan
glepairsl.cfm
Mathematics Course 3
Textbook Connection:
Chapter 7, Lessons:
2 & 5 and Lab 7-2
Mathematics Course 3
Textbook Online:
http://go.hrw.com/resour
ces/go_mt/hm3/so/c3ch7
aso.pdf
http://my.hrw.com/ma
th06_07/nsmedia/hom
ework_help/msm3/ms
m3_ch07_02_homewor
khelp.html
Volume 1 Issue 6
Dear Parents
Below you will find a list of concepts that your child will use and understand while completing
Unit 6 Congruency. Also included are references, vocabulary and examples that will help you
assist your child at home.
Concepts Students will Use and Understand
• Parallel lines have the same slope and perpendicular lines have opposite, reciprocal slopes.
• When two lines intersect, vertical angles are congruent and adjacent angles are
supplementary.
• When parallel lines are cut by a transversal, corresponding, alternate interior and alternate
exterior angles and congruent.
• The length of segments formed by two non-parallel transversals cutting parallel line is
proportional to the distances of the parallel lines from the intersection of the transversal.
• Parallel lines can be constructed using the properties of parallel lines cut by a transversal.
Vocabulary
Adjacent angles- angles in the same plane that have a common vertex and a common side,
but no common interior points.
Alternate exterior angles- pairs of angles formed when a third line (transversal) crosses 2
lines. These angles are on opposite sides of the transversal and are outside the 2 lines.
Alternate interior angles- pairs of angles formed when a third line (transversal) crosses 2
lines. These angles are on opposite sides of the transversal and are inside the 2 lines.
Coincidental- two equivalent linear equations overlap when graphed.
Complimentary angles- Two angles whose sum is 90 degrees.
Congruent- having the same size, shape and measure. Two figures are congruent if all of
their corresponding measures are equal.
Equiangular- The property of a polygon whose angles are all congruent.
Equilateral- the property of a polygon whose sides are all congruent.
Intersecting lines- Two lines in a plane that cross each other. Unless two lines are
coincidental, parallel or skew, they will intersect at one point.
Linear pair- adjacent, supplementary angles. Excluding their common side, a linear pair
forms a straight line.
Opposite Reciprocals- reciprocals are 2 numbers that have a product of 1; opposites are
positive and negative
Parallel lines- two lines that lie in the same plane and do not intersect.
Perpendicular lines- two lines that intersect at a right angle.
Reflection line- a line that is the perpendicular bisector of the segment with endpoints at a
pre-image point and the image of that point after reflection.
Regular polygon- a polygon that is both equilateral and equiangular.
Same-side exterior angles- pairs of angles formed when a transversal crosses 2 lines.
These angles are on the same side of the transversal and outside the 2 lines. The angles are
supplementary.
Same-side interior angles- pairs of angles formed when a transversal crosses 2 lines.
These angles are on the same side of the transversal and inside the 2 lines. The angles are
supplementary.
Skew lines- two lines that do not lie in the same plane (cannot be parallel or intersect).
Supplementary angles- two angles whose sum is 180 degrees.
Transversal- a line that crosses two or more lines.
Vertical angles- two nonadjacent angles formed by interesting lines or segments.
IMPORTANT REMINDER
Report Cards will be sent home on
Thursday, March 20, 2008
Math 8 Unit 1 Probability
Symbols
≅ congruent
⊥ perpendicular
Example 1
Name all angles that are congruent to angle 3.
∠2and ∠7 are what type of angles?
parallel
Example 2
Additional Links
http://www.cliffsnotes.
com/WileyCDA/CliffsRe
viewTopic/Proportional
-Parts-ofTriangles.topicArticleId
-18851,articleId18813.html
Find the value of m.
m
3
m+5
4
Example 3
What is the slope of a line parallel to a line with the equation of y=-4x+7?
http://www.analyzema
th.com/Slope/Slope.ht
ml
What is the slope of a line perpendicular to a line with the equation of y=2x+8?
Example 1
Angle 2, angle 6, and angle 7.
They are alternate exterior angles.
Example 2
m m +5
=
3
4
4m=3m+15
Example 3
Parallel: m=-4
Perpendicular: m= −
1
2
m=15
Key