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.
Chapter 1 Student Notes
Chapter 1 TestTuesday, August 29th
1.1 Points, Lines and Planes
Point -
A
B
C
D
m
Line -
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
P
A
B C
Plane -
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
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
Draw and Label each of the following4. m intersects P at X
5. P and R intersect at m
1.2Segments
Objective:1) Learn the language of Geometry2) Become familiar with segments and segment
measure
Line Segment -
A
B
Betweenness of Points -
A
B C
Measure of a Segment -
M
N6
Segment Congruence -
R
S7
T
U7
Segment Congruence is marked on a figure in the following
manner.
CB
A
1212
Multiple Pairs of Congruent Segments
From the markings on the above figure, make 2 congruence statement.CB
DA
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
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
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
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
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: ____________
1.3Distance and Midpoint
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.
Distance on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
AB =
Find the length of each segment.
DistanceFormula
A(2, 2)B(-4, 1)
C(2, -4)
Find the length of each segment.
BC
Midpoint on a Number Line
Midpoint =
A B C D
-5 0 5
1. AB
Find the midpoint of each segment.
2. AD
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?
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
= ( ) = ( )
Midpoint on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
Find the midpoint of each segment.
1. BC
= ( ) = ( )
Midpoint on a Coordinate Plane
A(2, 2)B(-4, 1)
C(2, -4)
Find the midpoint of each segment.
2. AC
= ( ) = ( )
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
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
1.4Angle Measure
Ray -
E
DS
R
BA
Angle–
Angles and Points
Points _______________________________
G ____________________
H ____________________
E ____________________H
D
E
G
F
Naming Angles
H
D
E
G
F2
1. ________
2. ________
3. ________
4. ________
Name the angle at the right as many ways as possible.
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. _______
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, __________________ ____________________________________
Types of Angles
Right angle:
________ different types of angles:
Acute angle:
Types of Angles
Obtuse angle: Straight angle:
Can also be called __________ ________________.
Congruent Angles
33o
33oM
W
Multiple Sets of Congruent Angles
__________
__________
A B
CD
KM is an angle bisector.
Angle Bisector
64
J
K
M
L
What conclusion can you draw about the figure at the right?
_________________
or
________________
When you want to add angles, use ______________________ _____________________________________________________________..
If you add m1 + m2, what is your result?_____________________________.
Adding Angles
●●●
21
J
K
M
L28o48o
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
Draw your own diagram and answer this question:
If ML is an angle bisector of PMY and mPML = 87, then find:
mPMY = _______mLMY = _______
Example
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 = _____
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 = ___
1-5Angle Pairs
Complementary Angles -
Examples:
21
M
N T
DR
S
Perpendicular – _______________________
Supplementary Angles-
Examples:
J
GL
K
21
KH
Adjacent Angles
Adjacent Angles
43
Vertical Angles-
Example:
A
E
D
C
B
12
4
3
Theorem:
●●● A
E
D
C
B
12
4
3
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.
Examples1. 1 & 2 are complementary. m1 = 4x + 5,
m2 = 5x + 4. Find x and the measure of each angle.
x = _____
m1 = _____ m2
= _____
Examples
2. 5 & 6 are supplementary. m5 = 10x + 12,
m6 = 2x + 6. Find x and the measure of each angle.
x = _____
m5 = _____ m6
= _____
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 = _____
2 1 3
4
Examples4. m2 = 5x + 12, m4 = 7x – 20. Find x and the measure of each angle.
x = _____
m 2 = _____
m1 = _____
1.6Polygons
Determine if each figure is a polgyon
Polygon -
Example of Concave PolygonsConcave Polgons
Examples of Convex Polygons
Convex Polygons
Number of Sides3456789
10111213n
Name of Polygon Hint
Examples of Regular Polygons
Regular Polygon-
Find the perimeter of each polygon.
Perimeter - distance around a polygon
Square RectangleRegular Hexagon
P = _______
8in
6cm
3cm
P = ______
4ft
P = ________
Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.
Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.
Find the perimeter and area of the polygon below.
3cm
3cm
8cm
8cm
5cm
5cm
5cm5cm
P = ________
A = ________
1. A(-3, 0), B(0, 4), C(4, -3)
Triangle ABC has the following coordinates. Find the perimeter of ABC.
P = _______