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