1. Measuring Angles (4).notebook October 21, 2014
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1 IWBAT estimate, classify, measure and draw acute, obtuse, right, straight, 180+, complementary, supplementary, and vertical angles. 1
2 Angles are measured in degrees! 2
3 Please Create a Vocabulary section for unit 3 Angle Types NAME DEFINITION EXAMPLE PICTUR Acute angle angle less than 90 Right angle angle equal to 90 Obtuse angle angle between 90 and 180 Straight angle angle equal to 180 Reflex angle angle greater than 180, less than 360 3
4 I do Angle Notation B vertex Symbols: B Read: "angle B" 4
5 I do Angle Notation It can also look like this! B C A Symbols: B, ABC, OR CBA Read: "angle B," "angle ABC, " or "angle CBA" 5
6 Angle Notation W Y X Z What color is angle WXY? What color is angle YXZ? What color is angle ZXW? 6
7 What is a protractor? A protractor is a tool that helps us measure angles. 7
8 Measuring angles correctly is important because it helps us build things like this: 8
9 Not this: 9
10 10
11 Drawing Angles Draw each angle type in your notes: acute angle right angle obtuse angle straight angle reflex angle 11
12 Measuring an Angle Step 1: Determine if the angle is acute, obtuse, right, or straight before using the protractor. Give yourself an estimate. Write down these steps! 12
13 Acute, Obtuse, Right, or Straight? 13
14 Acute, Obtuse, Right, or Straight? 14
15 Acute, Obtuse, Right, or Straight? 15
16 We can estimate the measure of an angle by visually comparing it to a 90 angle and a 180 angle
17 Check for Understanding Which is the best estimate of the measure of this angle?
18 Measuring an Angle Step 2: Place the Center Mark of the Protractor on the Vertex of the Angle (where the two lines meet) 18
19 Step 3: Rotate the zero edge so that it is on top of the horizontal line 19
20 Step 4: Read the angle measurement, compare with your estimate, and record. 20
21 Putting it all together... 21
22 Putting it all together... 22
23 Putting it all together... What about this??? 23
24 Independent Practice Before you measure each angle: 1.) Classify each angle as acute/right/obtuse/ straight/reflex 2.) ESTIMATE the angle measure Only THEN can you measure the angle using your protractor 24
25 DOL 1. Correctly name each angle measurement: a. 9 b. 250 c. 90 d. 180 e Measure problems 4,5,6 in your independent practice and label correctly. 25
26 Acute angles Using your ruler, draw AB 64 mm long Using your protractor, mark a 38 angle off of vertex A Using your ruler, draw AC 8.8 cm long Pass to your shoulder partner and have them check your work 26
27 C 8.8 cm = 88 mm A mm = 6.4 cm B What are the 3 names we could call this angle? 27
28 Right Angles Draw XY 2 cm long. Then draw YZ 1.5 cm long perpendicular to XY. Complete XYZ by drawing XZ. How long is XZ? Mark the right angle with the appropriate sign 28
29 Z 2.5 cm 1.5 cm X 2 cm Y Perpendicular lines make right angles 29
30 Obtuse Angles Create a triangle that includes 1 obtuse angle. What conjecture can you make about the other angles? 30
31 Straight Angles straight lines Straight lines make a half circle. How many degrees are in a straight angle? 31
32 Straight Angles D A B C If the m ABD is 127, name and find the measure of the acute angle 32
33 Straight Angles with a triangle D A B C You now know the m DBC Angle BDC is 47.5 Can you calculate the measure of angle DCB? 33
34 Find the measures of all the angles E 38 F 61 G 34
35 35
36 Circle Angles add up to 360 degrees Find the missing angles 36
37 Interesting, All 3 angles in a triangles add up to 180 degrees. All straight lines measure 180 degrees. All circle measure 360 degrees. All 4 angles in a quadrilateral add up to
38 Summary: Right angles = 90 degrees. Straight lines = 180 degrees. If 2 angles create a right angle or a straight line, they are given special names. 38
39 A C B D G E F H ABC + CBD = 90 EFG + GFH =
40 Complementary Angles 1. What is the measure of angle B? 63 B 2. What is the complement of an angle that measures 72 degrees? 40
41
42 Supplementary Angles 1. What is the measure of angle B? B 2. What is the supplement of an angle that measures 72 degrees? 42
43
44 44
45 Alternate Interior transversal Must have 2 parallel lines Must have a transversal 45
46 Alternate Exterior transversal Must have 2 parallel lines Must have a transversal 46
47 a.) name a pair of vertical angles b.) name a pair of supplementary angles a.) d.) name a pair of alternate exterior angles 47
48 Activity There are 10 objects around the room with marked angles. It is you and your partner's job to find the angle measures using your protractors. 48
49 Find the measure of each missing angle If we are given 2 parallel lines and a transversal, 8 angles are created. We only need to be given 1 measurement. The rules of geometry allow us to calculate all the remaining angles. 49
50 Do you think these lines are parallel? mathematically prove your answer 50
51 Point! Which way is vertical from you? 51
52 and 3 are congruent: alternate interior 1 and 2 are supplementary Therfore, 2 and 3 are supplementary 52
53 53
54 54
55 Check for Understanding 1. Acute or obtuse? A pair of angles that are 25.5 and are called what type of angles? 3. Find the measure of angle x and y 55
56 Vertical Angles Vertical angles are across from each other Vertical angles are congruent (the same) Do you see the circle? 56
57 Extension: If there are 4 angles at a point and they are in the ratio of 3:4:5:6, what is the size of the smallest angle? a. 18 c. 54 b. 20 d
58 Extension Do you see the trapezoid? 58
59 DOL 1.) What is wrong with this picture? 2a.) ) Find the measurement of all the remaining angles. 68 A B C D 2b.) If angle 2 is 126 degrees, how much do angles 1, 3, 4, and 5 add up to? 59
60 60
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