Chapter 9 Notes - Dripping Springs Independent School District
Download
Report
Transcript Chapter 9 Notes - Dripping Springs Independent School District
Chapter 9 Notes
9-1 Intro. To Geometry
H
W
T
Name four Points.
K
Name four different segments.
Write five other names for line n.
Name five different rays.
n
9-1 Intro. To GeometryAnswers
H
W
K
n
T
Name four Points. H,K, T, and W
Name four different segments. HT, WT, KT, WK
Write five other names for line n. WK, TK, KT, KW,
TW
Name five different rays. TH, TW, TK, WK, KW
Intersecting, Parallel, and
Skew Lines
R
Q
S
P
L
M
K
N
Name all indicated segments -•That intersect MN.
•That are skew to MN.
Intersecting, Parallel, and
Skew Lines-answers
R
Q
S
P
L
M
K
N
Name all indicated segments -•That intersect MN. ML, NK, MR, NS
•That are skew to MN. PS, RQ, PK, QL
9-2 Angle Relationships and
Parallel Lines
5
6
8
7
Name vertical angles.
Name adjacent angles.
If m<8 = 20°, find measures of <5, <6, and
<7.
9-2 Angle Relationships and
Parallel Lines-answers
5
6
8
7
Name vertical angles. 7,5; 8,6
Name adjacent angles. 5,8; 8,7;7,6; 6,5
If m<8 = 20°, find measures of <5, <6, and
<7. m<5 = 160°, m<6 = 20°, m<7 = 160°
9-2 Angle Relationships and
Parallel Lines
1
p
2
3
q
4
1.
2.
3.
4.
5.
6.
5
6
7
8
Name adjacent angles.
Name vertical angles.
Name supplementary angles.
Name complementary angles.
Name congruent corresponding angles.
Name congruent alternate interior angles.
p || q
9-2 Angle Relationships and
Parallel Lines
1
p
2
3
q
4
1.
2.
3.
4.
5.
6.
5
6
p || q
7
8
Name adjacent angles. 1,5; 1, 2; 2, 6; 6, 5
Name vertical angles. 3,8; 4,7; 2,5; 1,6
Name supplementary angles. 3,7; 4,8; 2,6; 5,6
Name complementary angles. none
Name congruent corresponding angles.1,3; 5,7; 2,4; 6,8
Name congruent alternate interior angles. 2,7; 6,3
9-2 Angle Relationships and
Parallel Lines
(5x -18)°
M
N
(4x+7)° P
R
1. Write an equation.
2. Find x.
3. Find m<MNQ.
4. Find m<MNR.
Q
9-2 Angle Relationships and
Parallel Lines-answers
(5x -18)°
M
Q
N
(4x+7)° P
R
1. Write an equation. 5x - 18 = 4x + 7
2. Find x. x=25
3. Find m<MNQ. 107°
4. Find m<MNR. 73°
9-3 Classifying Polygons
9-3 Classifying Polygonsanswers
Isoceles
acute
Right isosceles
Not a polygon
Scalene obtuse
Not a polygon
trapezoid
parallelogram
Equilateral acute
Classifying Quadrilaterals and
polygons
Classifying Quadrilaterals and
polygons-answers
Regular
Octagon
Regular
hexagon
parallelogram
square
rhombus
Regular
pentagon
trapezoid
rectangle
9-5 Congruence
Congruent figures: have the same size and shape
and their corresponding parts have equal measure.
•
•
D
B
C
A
E
F
ABC is congruent to
FDE
<A is congruent to <F
<B is congruent to <D
<C is congruent to <E
AC is congruent to FE
AB is congruent to FD
BC is congruent to DE
Identifying Congruent
Triangles
•
•
•
SSS: Side-Side-Side
SAS: Side-Angle-Side
ASA: Angle-Side-Angle
Examples: following slide.
Answers
9. <B congruent to <D
BC congruent to DC
<ABC congruent to <ECD
ASA
10. JK congruent to JM
LK congruent to LM
JL congruent to JL
SSS
9-6 Circles
•
•
•
•
Circle: is a set of all points in a plane that are the
same distance from a given point called the center
of the circle.
Radius: is a segment that has one endpoint at the
center and the other point on the circle
Diameter: is a chord that passes through the center
of a circle.
Chord: is a segment whose endpoints are on the
circle.
Circumference of a Circle
•
Circumference: the distance around a circle
•
2.
C = πd
C = 2πr
Find circumference of each circle.
Radius = 3.5 cm
Diameter = 1/2 yd
100 in.
3.
Radius = 4 2/3 ft.
•
1.
Circumference of a Circle answers
•
Circumference: the distance around a circle
•
2.
C = πd
C = 2πr
Find circumference of each circle.
Radius = 3.5 cm = 21.98cm
Diameter = 1/2 yd = 1 4/7 yd.
100 in.
3.
Radius = 4 2/3 ft. = 29 1/3 ft.
•
1.
C=314in
Central Angles
•
•
Central angle: is an angle whose vertex is the
center of a circle. There are 360o in a circle.
Examples: Find central angle.
•
•
•
•
•
1. 35% = _____ degrees
2. 50% = _____ degrees
3. 1% = ______ degrees
4. 30% = ______ degrees
5. 18% = ______ degrees
Central Angles-answers
•
•
Central angle: is an angle whose vertex is the center of a
circle. There are 360o in a circle.
Examples: Find central angle.
•
•
•
•
•
1. 35% = __126___ degrees
2. 50% = _180____ degrees
3. 1% = ____4__ degrees
4. 30% = ___108___ degrees
5. 18% = ___65___ degrees
9-8 Translations
•
•
•
•
•
Transformation: is a change of position or
size of a figure
Translation: is a transformation that moves
points the same distance and in the same
direction
A’: means A prime
B’: means B prime
These are the new figures after they have
been translated.
(1,4)
(-2,3)
(1,2)
Dilations
Dilation: a transformation that changes the
size of the figure but not usually the shape
Scale Factor: how many times larger or
smaller you will make the original figure
9-9 Symmetry and Reflections
•
Reflectional Symmetry: when one half is a
mirror image of the other half.
•
Line of symmetry: divides a figure into 2
congruent halves.
•
Reflection: is a transformation that flips a
figure over a line of reflection
9-10 Rotations
•
•
•
•
Rotations: is a transformation that turns a
figure about a fixed point
Center of rotation: this is the fixed point
where a figure is turned
Angles of rotation: the angle measure of the
rotation
Rotational symmetry: rotating a figure 180o,
or less, so that its image matches the original
figure