Download Introduction to Geometry

Introduction to Geometry
Name:
Points, Lines & Planes
Vocabulary

Angle (  ):

Collinear:

Coplanar:

Endpoint:

Intersection (∩):

Line (  ):

Line Segment/Segment( ):

Plane:

Point:

Ray( 
 ):

Triangle (∆):

Union (  ):

Vertex:
Examples:
Use the diagram to answer the following questions.
1. How many lines are shown?
2. Name these lines.
3. Where do 
 and 
 intersect?
AC
DE
 intersect 
 ? ( 
 ∩ 
 = ____)
4. Where does 
AC
BC
AC
BC
 and 
 ? ( 
  
 = ____)
5. What is the union of 
BA
BD
BA
BD
1
Rev D
Introduction to Geometry
Name:
Linear Measure & Precision
Vocabulary

Betweenness of Points:

Congruent (  ):

Distance:

Greatest possible error:

Measure:

Midpoint:

Noncollinear:

Percent of Error:

Precision:

Tick Marks:

Tolerance:
Collinear vs non-collinear
Triangle Inequality: For any 3 points there are only 2 possibilities
 3 points are collinear
 3 points are noncollinear & determine a triangle.
Examples:
1. For each diagram, tell whether x is between P and R.
a.
b.
2. For each diagram, tell whether x is the midpoint of AB.
a.
b.
c.
c.
3. Draw a diagram in which A, B and C are collinear, A, D and E are collinear and B, C, D are
noncollinear.
4. Find x and RS if S is between R and T, RS = 5x, ST = 3x and RT = 48.
5. Find x and ST if S is between R and T, RS = 4x-1, ST = 2x -1 and RT = 5x.
2
Rev D
Introduction to Geometry
Name:
Precision/Error Analysis
Error Analysis Examples:
1. Measurement: 57 mm
Precision: 1mm
Greatest Possible error: 0.5mm
Percent of Error: 0.5/57 * 100% = 0.88%
2. Measurement: 2 ¼ in or 2.25 in
Precision: 1/4 in
Greatest Possible Error: 1/8 in or 0.125 in
Percent of Error: 0.125/2.25 * 100% = 5.56%
Error Analysis Practice:
3. Measurement: 5 millimeters
Precision:
Greatest Possible error:
Percent of Error:
4. Measurement: 8 ½ inches or 8.5 in
Precision:
Greatest Possible Error:
Percent of Error:
Assumptions
Assumptions: Are they good or bad?
There are very specific things we need to look for when we are making assumptions.
We can assume the following
 Straight lines & angles are as they appear
 Collinearity of points
 Betweenneess of points
 Relative positions of points
 Adjacent  , linear pairs, supplementary 
We cannot assume the following
 Right angles
 Congruent segments
 Congruent angles
 Relative size of segments & angles
 Perpendicular Lines
Assumption Examples:
6. Should we assume that S, T and V are collinear in the diagram?
7. Should we assume that  S = 90º?
8. Name all points collinear with E &F.
9. Are G, E and D collinear? Are F and C collinear?
10. Which 2 segments do the tick marks indicate are congruent?
11. Is  A   D?
12. Is  F   ABF?
13. Name all points between F and D.
3
Rev D
Introduction to Geometry
Name:
Angle Measure
Vocabulary

Acute Angle:

Angle (  ):

Angle Bisector:

Congruent Angles:

Degree (º):

Obtuse Angle:

Opposite Rays:

Protractor:

Right Angle:

Straight Angle:

Vertex:
Examples
1. Use the protractor to find the measure of the angle. Then classify the
2.
angle as acute, obtuse, or right.
a.
b.
c.
 DEG = 80º,  DEF = 50º,
 KJM = 120º and  HJK = 90º.
Draw a conclusion about  FEG &
 HJM.
3.  HGF is a right angle,  HGE = (3x + 4)º,  EGF = (x + 6)º. Find
m  HGE.
4.

 bisects DGF , if DGE = 4x + 15 & EGF = 6x – 5,
GE
find DGE and classify the type of angle.
H
D
5. If  DGF is acute,
a. What are the restrictions on m  DGF?
E
F
G
b. What are the restrictions on x?
4
Rev D
Introduction to Geometry
Name:
Degree Conversions

60’ = 1º (60 minutes equals 1 degree)

60” = 1’ (60 seconds equals 1 minute)

90º = 89º 60’ = 89º 59’ 60”

180º = 179º 60’ = 179º 59’ 60”
Change to degrees and minutes
a. 87
c. 89
b. 60.
Change to degrees, minutes and seconds
a. 180
b. 46 7/8
Change to degrees
a. 41 24’
b. 19 45’
c. 78 15’
Operations with Degrees, Minutes, Seconds
Evaluate the following:
1. 490 32' 55" + 370 27' 15"
2. 430 15' 17" + 250 49' 18"
3. 900 - 370 66' 10"
4. 900 - 390 17"
5. 1800 - 1200 18'
6. 1800 - 980 52' 59"
5
Rev D
Introduction to Geometry
Name:
Angle Relationships
Vocabulary

Adjacent Angles:

Complementary Angles:

Linear Pair:

Perpendicular (  ):

Supplementary Angles:

Vertical Angles:
Algebraic Phrases
English Word Algebraic Translation
Complement
90 –x
Difference
Equal
=
Greater than
+, >
Increased by
+
Less than
-, <
English Word
Number
Opposite of a number
Product
Sum
Supplement
Algebraic Translation
N
-N
*
+
180 – x
Examples: Identification
Given the figure to the right, identify
1. Adjacent angles:
2. Vertical Angles:
3. Linear Pair:
Examples: Calculations
4. If FCD = 8x + 18, find x so that CF  CD
5. If  GCE = 90 and  GCF = 37º66’10”, find  FCE?
Examples: Translations
6. Find the measure of 2 complementary angles if the difference in measures of the 2 angles is 12.
7. Find the measures of 2 supplementary angels if the measure of 1 angle is 6 less than 5 times the
measure of the other angle.
8. Find the measure of two supplementary angles if the measure of one is 30 more than five times the
other.
9. The measure of the supplement of an angle is 40 more than 3 times the measure of its complement.
Find the measure of the angle.
6
Rev D