line geometric relationships
TRANSCRIPT
GeometricRelationshipspoint
hypothesisline
coplanarcollinear
parallel postulate
plane
conclusion
vertica
l angles
complementaryperpendicular
supplementary/
linear pair
Think about what you needfor class.... #1 YOUR BRAIN
#2 A 3ring binder with paper. I will give you a very indepth study guide for each unit (3 hole punched)
#3 pens & pencils
#4 A desire to learn and do your best and if you are confused, ask for help.
let's play
a vocabu
lary gam
e
Match each piece inyour envelope to thecorrect box on the next page.
Once you think youhave them all in theright spot, copy the definitions onto thepage.
Point Space Line Collinear
Plane Coplanar Postulate Segment
Parallel lines
Skew lines Parallel planesCongruentAngle
Midpoint Perpendicular Hypothesis
AnglesVertical
ComplementarySupplementary
Conclusion Angle bisector
Perpendicularbisector
Point Space Line Collinear
Plane Coplanar Postulate Segment
Parallel lines
Skew lines Parallel planesCongruentAngle
Midpoint Perpendicular Hypothesis
AnglesVertical
ComplementarySupplementary
Conclusion Angle bisector
Perpendicularbisector
a location or
coordinate
an endless 3D set
of points
an infinite set of
points extending
indefinitely both ways2 or more points that lie
on the same linea flat surface
extending in all
directions
2 or more lines that
lie on the same plane
a statement that
describes a relationship
part of aline consisting of 2
endpoints
2 rays that share
a common endpt
http://www.history.com/shows/stanleessuperhumans/videos/humancalculator#humancalculator
Scott Flansburg
also www.ted.com
arthur benjamin
http://www.youtube.com/watch?v=1LyoeWLmclU
"more than human"
Do you have MAD skills????
A location or coordinate.
An endless 3 dimensional set of points.
An infinite set of points that extends indefinately in bothdirections.Two or more points that lie on the same line.
A flat surface that extends indefinitely in all directions.
Two or more lines that lie on the same plane.
A statement that describes a relationship in geometry.
Part of a line that consists of 2 endpoints.
Two rays that share a common endpoint.
Lines that are not in the same plane they are neither parallel nor intersecting.
Equal in measure.Planes that never intersect.The middle of a line segment.
Forming a right angle.
The "if" part of a theorem or conditional.
Lines that never intersect.
The "then" part of a theorem or conditional.
A line or ray that splits an angle in half.
A line, ray, or segment that divides a segment in half, also creating a right angle.
Two angles that share a common vertex, but no common interior points. They open opposite from one another.
Angles whose sum is 90 degrees.
Angles whose sum is 180 degrees.
Bellringer:
Which of our vocabulary words do you think the term "linear pair" best relates to? ______________
Draw an example of what you think a linear pair looks like
If 2 planes, like the ceiling and the floor, are both perpendicular to a 3rd plane, like the wall, whatdo you know about those first 2 planes?
Important Notation and Symbols
1.) parallel 2.) perpendicular 3.) congruent
4.) line 5.) line segment 6.) ray
7.) approximately 8.) measure of an angle 9.) similar
10.) triangle 11.) Point 12. plane
1 234
5 678
which o
nes
appear
to be
congru
ent?
Important Theorems & Postulates:
1.) Vertical angles are congruent.Proof:
2.) Through any two points, there is exactly one line.Diagram:
3.) A line contains at least two points. Diagram:
123
4Given: <1 and <3 are vertical angles
Statements Reasons<1 and <3 are vertical angles 1.) Given
2.) <1 and <2 are a linear pair 2.) def'n linear pair
<2 and <3 are a linear pr.
3.) m<1 + m<2 = 180 3.) linear pair sum is 180
m<2 + m<3 = 180
1.)
4. If two lines intersect, their intersection is exactly one point. Diagram:
5.) If two planes intersect, their intersection is a line Find an example in the room and explain:
6.) If two lines are perpendicular to the same line, then they must be parallel:Find an example in the room and explain:
7.) All right angles are congruent. Ex:
8.) If two angles are complementary to the same or congruent angles, then they are congruent. Ex:
9.) If two angles are supplementary to the same or congruent angles, then they are congruent. Ex:
** also remember... which ones are "linear pairs" ?
moreimportant
postulates
10.) When a transversal crosses parallel lines, the following angle relationships are formed:a.) alternate interior angles are congruentb.) corresponding angles are congruentc.) alternate exterior angles are congruentd.) consecutive interior angles are supplementary
a
b
t
1 23 4
5 67 8
11.) Points on a perpendicular bisector of a line segment are exactly those equidistant from the segments endpoints.Diagram:
BELLRINGER1.) List the kinds of angles that are congruent when parallel lines are cut by a transversal:
2.) Find the x value that would make lines l and m parallel
9x 4
140
After the test is handed in......On a half sheet of paper draw and label this situation.
Two lines, m and n, are parallel to each other.Two other lines, a and b, are also parallel to each other and perpendicular to m and n.
Also write in the degree measure of each angle formed.