Chapter 8. Properties of Triangles and Quadrilaterals. 02/2017 LSowatsky
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1 Chapter 8 Properties of Triangles and Quadrilaterals 02/2017 LSowatsky 1
2 8-1A: Points, Lines, and Planes I can Identify and label basic geometric figures. LSowatsky 2
3 Vocabulary: Point: a point has no dimension. It is represented by a dot. A Line: A line has one dimension. Through any two points, there is exactly one line. B l A
4 Rays and line segments are parts of lines. A line segment has a definite beginning and end. 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 A B The symbol for segment AB is AB
5 Rays and line segments are parts of lines. A ray has a definite starting point and extends without end in one direction. A B 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. The symbol for ray AB is AB
6 B M A C 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.
7 Lines: Intersecting lines Perpendicular Lines Parallel Lines LSowatsky 7
8 Congruent: Same shape and size Symbol: LSowatsky 8
9 Identify the figures: 1) 4) P A F X 2) N 5) F M E 3) C D LSowatsky 9
10 Homework: p. 443 # /2017 LSowatsky 10
11 8-1B: Measuring Angles I can measure and classify angles. LSowatsky 11
12 There is another case where two rays can have a common endpoint. This figure is called an. angle S Some parts of angles have special names. The common endpoint is called the, vertex and the two rays that make up the sides of the angle are called the sides of the angle. R vertex side T
13 You can use a protractor to measure angles and sketch angles of given measure. 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. Q R S
14 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 obtuse angle 90 < m A < 180 A right angle m A = 90 A acute angle 0 < m A < 90
15 Classify each angle as acute, obtuse, or right Obtuse Right Acute Acute Obtuse Acute
16 Homework: p. 448 # /2017 LSowatsky 16
17 8-1C: Angle Relationships I can classify and apply angle relationships LSowatsky 17
18 When two lines intersect, four angles are formed. There are two pairs of angles across from each other. These pairs are called. vertical angles Vertical angles are congruent! LSowatsky 18
19 Supplementary angles: Two angles whose sum is 180 o LSowatsky 19
20 Complementary Angles: Two angles whose sum is 90 o LSowatsky 20
21 Example: Classify the angles as complementary, supplementary, or neither 1) 120º 60º 3) 2) 40º 60º 30º 60º LSowatsky 21
22 Find the missing angles. 1) 2)?º 83º?º 62º LSowatsky 22
23 Find the missing angles. x o y o 25 o 30 o LSowatsky 23
24 Homework: p. 454 # /2017 LSowatsky 24
25 8-2B: Triangles I can classify triangles and find missing angles measures in triangles LSowatsky 25
26 Triangle: A figure with three sides and three angles. The sum of its angles is always 180 degrees. LSowatsky 26
27 acute triangle obtuse triangle right triangle Triangles Classified by Angles All angles are acute 1 obtuse angle, 2 acute 1 right angle, 2 acute
28 scalene isosceles equilateral Triangles Classified by Sides no sides congruent at least two sides congruent all sides congruent
29 Example: 1) Draw a right isosceles triangle. 2) Draw an acute scalene triangle. LSowatsky 29
30 Example: Find the missing angle. x 35 o 65 o 3/7/2017 LSowatsky 30
31 Find the missing angle x LSowatsky 31
32 Homework: Workbook p /2017 LSowatsky 32
33 Chapter 8 Midchapter Test LSowatsky 33
34 8-3B: Properties of Quadrilaterals I can classify quadrilaterals and find missing angles measures in quadrilaterals. LSowatsky 34
35 Make Graphic organizer LSowatsky 35
36 Identify the parallelogram below. Identify the parallelogram below. A B D Parallelogram ABCD has 4 right angles, but the four sides are not congruent. C rhombus Therefore, it is a rectangle
37 Use the Venn diagram to answer the following questions: T or F Quadrilaterals Parallelograms Rhombi Squares Rectangles 1) Every square is a rhombus: T 2) Every rhombus is a square: F 3) Every rectangle is a square: F 4) Every square is a rectangle: T 5) All rhombi are parallelograms: T 6) Every parallelogram is a rectangle: F
38 Sum of the interior angles of a quadrilateral is always 360 o LSowatsky 38
39 Example: Find the missing angle measurement. ABCD is a parallelogram. Find the m D LSowatsky 39
40 Homework: Workbook p /2017 LSowatsky 40
41 8-3C: Properties of Polygons I can classify polygons and find the sum of angle measures in a polygon. LSowatsky 41
42 Polygons The word polygon means many angles A two dimensional object A closed figure
43 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
44 Examples of Polygons
45 These are not Polygons
46
47 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
48 Find the measure of the interior angles of the regular octogon.
49 Exterior angle the angle between any side of a figure and a line extended from an adjacent side. (aka outside angle) LSowatsky 49
50 Homework: p. 477 #7-25odd, 34 37all 02/2017 LSowatsky 50
51 8-3D: Similar and Congruent Figures I can identify similar and congruent figures. LSowatsky 51
52 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
53 Corresponding Parts: Corresponding sides: sides of similar or congruent figures that are in the same relative position. B E A C D F Corresponding angles: angles of similar or congruent figures that are in the same relative position. LSowatsky 53
54 1. Which of these shapes are congruent to the yellow one?
55 Congruent shapes are all shown in yellow were you right?
56 Similar shapes
57 Which of these shapes are similar to the yellow one?
58 Start page Similar shapes are all shown in yellow were you right?
59 Identify similar figures: LSowatsky 59
60 Homework: p.483 #1 23 odd, 29 02/2017 LSowatsky 60
61 Coordinate Plane Basics I can draw a coordinate plane, label quadrants, and plot ordered pairs. LSowatsky 61
62 Ordered pairs are used to locate points in a coordinate plane. y-axis (vertical axis) x-axis (horizontal axis) origin (0,0)
63 Quadrants: LSowatsky 63
64 In an ordered pair, the first number is the x-coordinate. The second number is the y- coordinate. Graph. (-3, 2)
65 What is the ordered pair for A? 1. (3, 1) 2. (1, 3) 3. (-3, 1) -5 5 A 5 4. (3, -1) -5
66 What is the ordered pair for B? 1. (3, 2) 5 2. (-2, 3) 3. (-3, -2) 4. (3, -2) -5 B 5-5
67 What is the ordered pair for C? 1. (0, -4) 2. (-4, 0) 3. (0, 4) 4. (4, 0) C 5
68 What is the ordered pair for D? 1. (-1, -6) 5 2. (-6, -1) 3. (-6, 1) 4. (6, -1) -5 D -5 5
69 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 D -5 5 C A B 5
70 Homework: worksheets 02/2017 LSowatsky 70
71 8-4B: Translations I can graph translations on a coordinate plane. LSowatsky 71
72 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 LSowatsky 72
73 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
74 Example: translate figure 8 units down. LSowatsky 74
75 Homework: Workbook p /2017 LSowatsky 75
76 8-4C: Reflections I can graph reflections on a coordinate plane. LSowatsky 76
77 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
78 Whiteboard practice LSowatsky 78
79 Homework: Workbook p. 139 &140 02/2017 LSowatsky 79
80 8-4D: Rotations I can graph rotations on a coordinate plane. LSowatsky 80
81 Rotations: turn the geometric figure Dependent on: Direction (clockwise vs. counterclockwise) Degree (90, 180, 270, 360 multiples of 90) LSowatsky 81
82 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
83 Whiteboard Practice LSowatsky 83
84 Homework: Workbook p /2017 LSowatsky 84
85 Chapter 8 Test LSowatsky 85
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