chapter 8mrssowatskysmath.weebly.com/uploads/1/3/3/0/13301598/6th... · 2019-11-29 · 8-1a:...
TRANSCRIPT
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Chapter 8
Properties of Triangles and Quadrilaterals
02/2017 1 LSowatsky
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8-1A: Points, Lines, and Planes
I can…
Identify and label basic geometric figures.
LSowatsky 2
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Vocabulary:
Point: a point has no dimension. It is represented by a dot.
Line: A line has one dimension. Through any two points, there is exactly one line.
A
A
B
l
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• A line segment is part of a line containing two endpoints
and all points between them.
•A line segment is named using
its endpoints.
•The line segment is named
segment AB or segment BA
•The symbol for segment AB is
A B
Rays and line segments are parts of lines.
A ___________ has a definite beginning and end. line segment
AB
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A ___ has a definite starting point and extends without end in one direction.
ray
RAY: The starting point of a ray is called the ________. endpoint
A ray is named using the endpoint first, then another point on the ray.
The ray above is named ray AB.
A B
Rays and line segments are parts of lines.
The symbol for ray AB is AB
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Plane: a plane has two dimensions. It is represented by a shape that looks like piece of paper, but extends without end.
Use three points to name a plane.
A
B
C
M
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Lines:
LSowatsky 7
Intersecting lines Perpendicular Lines Parallel Lines
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Congruent:
Same shape and size
Symbol:
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Identify the figures:
1) 4)
2) 5)
3)
LSowatsky 9
P
X
A
M
N
C
D
F
E
F
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Homework:
p. 443 #1 - 25
02/2017 LSowatsky 10
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8-1B: Measuring Angles
LSowatsky 11
I can… measure and classify angles.
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There is another case where two rays can have a common endpoint.
R
S
T
This figure is called an _____. angle
Some parts of angles have special names.
The common endpoint is called the ______, vertex
vertex and the two rays that make up the sides of the angle are called the sides of the angle.
side
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You can use a _________ to measure angles and sketch angles of given measure.
protractor
Q
R S
1) Place the center point of the protractor on vertex R. Align the straightedge with side RS.
2) Use the scale that begins with 0 at RS. Read where the other side of the angle, RQ, crosses this scale.
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Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle
m A = 90
acute angle
0 < m A < 90
A
obtuse angle
90 < m A < 180
A
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Classify each angle as acute, obtuse, or right.
110°
90° 40°
50°
130° 75°
Obtuse
Obtuse
Acute
Acute Acute
Right
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Homework:
p. 448 #1 - 27
02/2017 LSowatsky 16
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8-1C: Angle Relationships
LSowatsky 17
I can… classify and apply angle relationships
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When two lines intersect, ____ angles are formed. four
1 2
3 4
There are two pairs of angles across from each other.
These pairs are called _____________. vertical angles
LSowatsky 18
Vertical angles are congruent!
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Supplementary angles:
Two angles whose sum is 180o
LSowatsky 19
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Complementary Angles:
Two angles whose sum is 90o
LSowatsky 20
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Example: Classify the angles as complementary, supplementary, or neither
1) 3)
2)
LSowatsky 21
60º 120º
60º 30º
60º 40º
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Find the missing angles.
1) 2)
LSowatsky 22
83º ?º
62º
?º
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Find the missing angles.
LSowatsky 23
30o
25o yo
xo
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Homework:
p. 454 #9 - 35
02/2017 LSowatsky 24
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8-2B: Triangles
LSowatsky 25
I can… classify triangles and find missing angles measures in triangles
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Triangle:
A figure with three sides and three angles.
The sum of its angles is always 180 degrees.
LSowatsky 26
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Triangles
Classified by
Angles
60°
80°
40°
acute triangle
All angles are acute
obtuse triangle
right triangle
1 obtuse angle, 2 acute
1 right angle, 2 acute
17°
43°
120°
30°
60°
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Triangles
Classified
by
Sides
scalene isosceles equilateral
no ___ sides
congruent
__________ sides
congruent
___ sides
congruent
at least two all
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Example:
LSowatsky 29
1) Draw a right isosceles triangle.
2) Draw an acute scalene triangle.
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Example: Find the missing angle.
LSowatsky 30 3/7/2017
x
35o 65o
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Find the missing angle.
LSowatsky 31
370
x
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Homework:
Workbook p. 127
02/2017 LSowatsky 32
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Chapter 8 Midchapter Test
LSowatsky 33
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8-3B: Properties of Quadrilaterals
I can…
classify quadrilaterals and find missing angles measures in quadrilaterals.
LSowatsky 34
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Make Graphic organizer
LSowatsky 35
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Identify the parallelogram below.
D C
B A
Parallelogram ABCD has 4 right angles, but the four
sides are not congruent.
Therefore, it is a _________ rectangle
Identify the parallelogram below.
rhombus
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Quadrilaterals
Parallelograms
Rhombi Rectangles Squares
Use the Venn diagram to answer the following questions: T or F
1) Every square is a rhombus: ___
2) Every rhombus is a square: ___
3) Every rectangle is a square: ___
4) Every square is a rectangle: ___
5) All rhombi are parallelograms: ___
6) Every parallelogram is a rectangle: ___
T
T
T F
F
F
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Sum of the interior angles of a quadrilateral is always 360o
LSowatsky 38
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Example: Find the missing angle measurement.
LSowatsky 39
ABCD is a parallelogram. Find the m D
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Homework:
Workbook p. 131
02/2017 LSowatsky 40
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8-3C: Properties of Polygons
I can…
classify polygons and find the sum of angle measures in a polygon.
LSowatsky 41
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Polygons
The word polygon means “many
angles”
A two dimensional object
A closed figure
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More about Polygons
Made up of three or more straight line
segments
There are exactly two sides that meet at a
vertex
The sides do not cross each other
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Examples of
Polygons
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These are not Polygons
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Interior angle: An angle on the inside of the
polygon.
Sum of interior angles of a polygon:
D = (n-2)180 Note: n is the number of sides
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Find the measure of the interior angles of the regular octogon.
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Exterior angle – the angle between any side of a figure and a line extended from an adjacent side. (aka outside angle)
LSowatsky 49
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Homework:
p. 477 #7-25odd, 34 – 37all
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8-3D: Similar and Congruent Figures
I can…
identify similar and congruent figures.
LSowatsky 51
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Similar Figures: figures with the same shape, but can be different sizes; all angles are congruent
Congruent Figures: figures with the same size and shape.
LSowatsky 52
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Corresponding Parts:
Corresponding sides: sides of similar or congruent figures that are in the same relative position.
Corresponding angles: angles of similar or congruent figures that are in the same relative position.
LSowatsky 53
E
DA
B
CF
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1. Which of these shapes are congruent to the yellow one?
2
5
4
3
1
7 6
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Congruent shapes are all shown in yellow – were you right?
5
4
3
1
7 6
2
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Similar shapes
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Which of these shapes are similar to the yellow one?
2
5
4
3
1
7 6
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Similar shapes are all shown in yellow – were you right?
2
5
4
3
1
7 6
Start page
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Identify similar figures:
LSowatsky 59
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Homework:
p.483 #1 – 23 odd, 29
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Coordinate Plane Basics
I can…
draw a coordinate plane, label quadrants, and plot ordered pairs.
LSowatsky 61
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Ordered pairs are used to locate points in a coordinate plane.
x-axis (horizontal axis)
origin (0,0)
y-axis (vertical axis)
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Quadrants:
LSowatsky 63
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In an ordered pair, the first number is the x-coordinate. The second number is the y-coordinate. Graph. (-3, 2)
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What is the ordered pair for A?
1. (3, 1)
2. (1, 3)
3. (-3, 1)
4. (3, -1)
5
5
-5
-5
• A
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What is the ordered pair for B?
5
5
-5
-5
• B
1. (3, 2)
2. (-2, 3)
3. (-3, -2)
4. (3, -2)
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What is the ordered pair for C?
1. (0, -4)
2. (-4, 0)
3. (0, 4)
4. (4, 0)
5
5
-5
-5
• C
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What is the ordered pair for D?
5
5
-5
-5
• D
1. (-1, -6)
2. (-6, -1)
3. (-6, 1)
4. (6, -1)
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Write the ordered pairs that name points A, B, C, and D.
A = (1, 3)
B = (3, -2)
C = (0, -4)
D = (-6, -1)
5
5
-5
-5
• A
• B
• C
• D
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Homework:
worksheets
02/2017 LSowatsky 70
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8-4B: Translations
I can…
graph translations on a coordinate plane.
LSowatsky 71
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Vocabulary: Transformations – a movement of a geometry shape
Preimage – the image before the transformation (original figure)
Image – the figure after the transformation
New points are called primes
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Translations:
A slide of the preimage where each point moves the same distance in the same direction
2 ways to find new points (primes)
1) use a graph
2) calculate new coordinates
LSowatsky 73
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LSowatsky 74
Example: translate figure 8 units down.
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Homework:
Workbook p. 137
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8-4C: Reflections
I can…
graph reflections on a coordinate plane.
LSowatsky 76
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Reflection - A ‘flip’ over a line of reflection to create a mirror
image (each point is moved to other side of line
To find ‘prime’ points of the image: If it reflects over the x-axis, x value stays same and y-
value if opposite sign
If it reflects over the y-axis, x value is the opposite sign and y value stays the same
LSowatsky 77
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Whiteboard practice
LSowatsky 78
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Homework:
Workbook p. 139 &140
02/2017 LSowatsky 79
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8-4D: Rotations
I can…
graph rotations on a coordinate plane.
LSowatsky 80
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Rotations: turn the geometric figure
Dependent on: Direction (clockwise vs. counterclockwise)
Degree (90, 180, 270, 360 – multiples of 90)
LSowatsky 81
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Example: 90 rotation Look for pattern and compare ordered pairs of vertices
Preimage:
A (-5, 7) A’ (7, 5)
B (-1, 6) B’ (6, 1)
C (-3, 2) C’ (2, 3)
General Rule: For each clockwise 90 rotation, switch the x and y and change sign of y
LSowatsky 82
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Whiteboard Practice
LSowatsky 83
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Homework:
Workbook p. 141
02/2017 LSowatsky 84
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Chapter 8 Test
LSowatsky 85