think about this: tuesday, january 31,2012
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Think About This: Tuesday, January 31,2012. Partner Answers! . Are points E and C collinear? What is the intersection of plane ADCB and plane HGCD? Name the 4 th point in plane EHC. P. 33: 87-94. Solutions to Page 33. 87)never 88) never 89)always 90)never 91)always 92)always - PowerPoint PPT PresentationTRANSCRIPT
Think About This:Tuesday, January 31,2012
1. Are points E and C collinear?
2. What is the intersection of
plane ADCB and plane HGCD?
3. Name the 4th point in plane
EHC.
4. P. 33: 87-94
Partner Answers!
Solutions to Page 33
87)never 88) never 89)always 90)never 91)always 92)always 93)always 94)never
Parallel lines are coplanar lines that do not intersect.
These symbols indicate lines a and b are parallel.
a
b
a || b
Skew lines are noncoplanar; therefore, they are not parallel and do not intersect.
AB || EF
AB and CG are skew.
Parallel planes are planes that do not intersect.
Plane ABCD || Plane GHIJ
Today’s Goals…
Chapter 1 – Tools of Geometry
1.4 Measuring Segments and Angles
Two segments with the same length are congruent () segments.
If AB = CD, then AB CD
A B
2 cm
C D
2 cm
Stop and Think…AB + BC = 6 and AC = 6.
A B
C D E
Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and C, then AB + BC = AC.
A B C
Ex.1: If DT = 60, find the value
of x. Then find DS and ST.
DS + ST = DT (Segment Addition Postulate)
D S T
2x – 8 3x – 12
You Try… #1
EG = 100. Find the value of x. Then find EF and FG.
E F G
4x – 20 2x + 30
Midpoint A midpoint of a segment is a point that
divides a segment into two congruent segments.
A B C
AB BC
Ex.2: C is the midpoint of AB.
Find AC, CB, and AB.
AC = CB (Definition of midpoint)
A C B
2x + 1 3x – 4
You Try… #2
Z is the midpoint of XY, and XY = 27.
Find XZ.
Angle ()
Formed by two rays with the same endpoint.
The endpoint is the vertex of the angle.
Classifying Angles
Acute is between 0 and 90.
Right is equal to 90.
Obtuse is between 90 and 180.
Straight is equal to 180.
55
135
180
90
Angle Addition PostulatePART I:
If point B is in the interior of AOC, then mAOB + mBOC = mAOC.
A
B
CO
Angle Addition PostulatePART II:
If AOC is a straight angle, then:mAOB + mBOC = 180.
A O C
B
Ex.3a:What is mTSW if
mRST = 50 and mRSW = 125?
Ex.3b: If mDEG = 145, find mGEF.
D E F
G
You Try… #3
12
A
B C
Suppose that m1 = 42 and mABC = 88. Find m2.
Congruent AnglesAngles with the same measure
If m1 = m2, then 1 2.
55 55