Chapter 1 Test Tuesday, August 29 th. A B C D m.
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Transcript of Chapter 1 Test Tuesday, August 29 th. A B C D m.
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Chapter 1 Student Notes
Chapter 1 TestTuesday, August 29th
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1.1 Points, Lines and Planes
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Point -
A
B
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C
D
m
Line -
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Collinear -
• T / F A and B are Collinear
• T / F A and C are Collinear
• T / F A, B and C are Collinear
A B
C
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P
A
B C
Plane -
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Coplanar -A B
C D
G
E F
• Name 3 Coplanar Points ________
•Name 3 Noncoplanar Points _________
• T/F C, D and G are coplanar
• T/F A, B, E, F are coplanar
• T/F A, B, C, E are coplanar
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Draw and Label each of the following1. n and m intersect at P
2. p contains N
3. P contains A and B, but not C
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Draw and Label each of the following4. m intersects P at X
5. P and R intersect at m
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1.2Segments
Objective:1) Learn the language of Geometry2) Become familiar with segments and segment
measure
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Line Segment -
A
B
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Betweenness of Points -
A
B C
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Measure of a Segment -
M
N6
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Segment Congruence -
R
S7
T
U7
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Segment Congruence is marked on a figure in the following
manner.
CB
A
1212
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Multiple Pairs of Congruent Segments
From the markings on the above figure, make 2 congruence statement.CB
DA
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1. AC = 4, AD = 3, Find CD = ______
2. CD = 15, AD = 7, Find AC = _____
A is between C and D. Find Each Measure.
C 4 A 3 D
C A 7 D
15
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3. AC = x + 1, AD = x + 3, CD = 3x – 5, Find x = _____
A is between C and D. Find Each Measure.
C x + 1 A x + 3 D
3x - 5
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1. AC = 8, AD = 5, Find CD = ______
2. CD = 20, AD = 12, Find AC = _____
A is between C and D. Find Each Measure.
C 8 A 5 D
C A 12 D
20
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3. AC = 2x + 1, AD = 2x + 3, CD = 5x – 10, Find x = ___
A is between C and D. Find Each Measure.
C 2x + 1 A 2x + 3 D
5x – 10
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C is between A and B in each figure. Select the figure that has AB = 12. Select all that apply.
A 8 C 4 B D 8 B A
A. C is between A and B. B. B is between A and D.
D B A
C. B is between A and D.AB = 2x + 5, BD = 3x + 4, AD = 6x – 3
D B A
D. B is between A and D.AB = 2x + 2, DB = 4x +2, DA =34
Answer: ____________
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1.3Distance and Midpoint
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Distance on a Number Line =
A B C D
-5 0 5
AB =
BC =
AD =
BD =
Use the number line to find the length of each segment.
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Distance on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
AB =
Find the length of each segment.
DistanceFormula
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A(2, 2)B(-4, 1)
C(2, -4)
Find the length of each segment.
BC
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Midpoint on a Number Line
Midpoint =
A B C D
-5 0 5
1. AB
Find the midpoint of each segment.
2. AD
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A B C D
-5 0 5
Find the midpoint of each segment.
3. BC
4. If A is the midpoint of EC, what is the location for point E?
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Midpoint on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
Midpoint = ( )x1 + x2 , y1 + y2
2 2
Find the midpoint of each segment.
1. AB
= ( ) = ( )
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Midpoint on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
Find the midpoint of each segment.
1. BC
= ( ) = ( )
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Midpoint on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
Find the midpoint of each segment.
2. AC
= ( ) = ( )
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M is the midpoint of AB. Given the following information, find the missing coordinates.
M(2, 6) , B(12, 10) , A ( ? , ? ) Midpoint = ( )x1 + x2 , y1 + y2
2 2
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M is the midpoint of AB. Given the following information, find the missing coordinates.
M(6, -8) , A(2, 0) , B ( ? , ? )Midpoint = ( )x1 + x2 , y1 + y2
2 2
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1.4Angle Measure
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Ray -
E
DS
R
BA
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Angle–
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Angles and Points
Points _______________________________
G ____________________
H ____________________
E ____________________H
D
E
G
F
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Naming Angles
H
D
E
G
F2
1. ________
2. ________
3. ________
4. ________
Name the angle at the right as many ways as possible.
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Naming Angles
32
J
K
M
L
Name the angles at the right as many ways as possible.
1. _______
2. _______
3. _______
4. _______
1. _______
2. _______
3. _______
4. _______
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Naming Angles
32
J
K
M
L
Name the angles at the right as many ways as possible.
1. _________
2. _________
3. _________
●●● ●
●●
There is more than one angle at vertex K, __________________ ____________________________________
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Types of Angles
Right angle:
________ different types of angles:
Acute angle:
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Types of Angles
Obtuse angle: Straight angle:
Can also be called __________ ________________.
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Congruent Angles
33o
33oM
W
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Multiple Sets of Congruent Angles
__________
__________
A B
CD
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KM is an angle bisector.
Angle Bisector
64
J
K
M
L
What conclusion can you draw about the figure at the right?
_________________
or
________________
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When you want to add angles, use ______________________ _____________________________________________________________..
If you add m1 + m2, what is your result?_____________________________.
Adding Angles
●●●
21
J
K
M
L28o48o
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Angle Addition Postulate The sum of the two smaller angles adjacent angles will
_______________________________________________________________________________________________.
Complete:
m ______ + m ______ = m _______
orm ______ + m ______ = m _______
21
R
S
U
T
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Draw your own diagram and answer this question:
If ML is an angle bisector of PMY and mPML = 87, then find:
mPMY = _______mLMY = _______
Example
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JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4. Find x and mLJM.
L
J M
K(4x + 10)o
(6x – 4)o
mLJM = _____
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RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x + 3. Find x and mPRS.
P
R T
S
(4x + 3)o
mPRS = ___
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1-5Angle Pairs
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Complementary Angles -
Examples:
21
M
N T
DR
S
Perpendicular – _______________________
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Supplementary Angles-
Examples:
J
GL
K
21
KH
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Adjacent Angles
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Adjacent Angles
43
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Vertical Angles-
Example:
A
E
D
C
B
12
4
3
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Theorem:
●●● A
E
D
C
B
12
4
3
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What’s “Important” in Geometry?4 things to always look for !
. . . and ___________( )Most of the rules (theorems)and vocabulary of Geometryare based on these 4 things.
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Examples1. 1 & 2 are complementary. m1 = 4x + 5,
m2 = 5x + 4. Find x and the measure of each angle.
x = _____
m1 = _____ m2
= _____
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Examples
2. 5 & 6 are supplementary. m5 = 10x + 12,
m6 = 2x + 6. Find x and the measure of each angle.
x = _____
m5 = _____ m6
= _____
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2 1 3
4
Examples
3. m1 = 2x + 7, m3 = 3x – 3. Find x and the measure of each angle.
Find x = _____
m 2 = _____
m1 = _____
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2 1 3
4
Examples4. m2 = 5x + 12, m4 = 7x – 20. Find x and the measure of each angle.
x = _____
m 2 = _____
m1 = _____
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1.6Polygons
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Determine if each figure is a polgyon
Polygon -
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Example of Concave PolygonsConcave Polgons
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Examples of Convex Polygons
Convex Polygons
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Number of Sides3456789
10111213n
Name of Polygon Hint
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Examples of Regular Polygons
Regular Polygon-
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Find the perimeter of each polygon.
Perimeter - distance around a polygon
Square RectangleRegular Hexagon
P = _______
8in
6cm
3cm
P = ______
4ft
P = ________
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Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.
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Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.
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Find the perimeter and area of the polygon below.
3cm
3cm
8cm
8cm
5cm
5cm
5cm5cm
P = ________
A = ________
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1. A(-3, 0), B(0, 4), C(4, -3)
Triangle ABC has the following coordinates. Find the perimeter of ABC.
P = _______