1. Estimate the size of each angle below. Then determine if it is acute, right, obtuse, or straight.
170 30 90 100 180
Find the measure of the following angles:
a. EDF = ___________
b. ADE = ___________
c. CDF = ___________
d. FDC = ___________
35145
100100
3. Complete the statements based on the markings in the picture.
a. LJK ___________
b. LMP ___________
c. JIH ___________
MJI
GHQ
PIG
In the picture, mMRT = 133.
a. Is MRT acute, right or obtuse?
b. Write an equation and solve for x.
c. Find the measure of MRN.
obtuse
6g – 11 = 133 g = 24
46
5. Construct a copy the following angle so that the angle is doubled. Be sure to leave all construction markings.
5. Construct a copy the following angle so that the angle is doubled. Be sure to leave all construction markings.
6. Construct the angle bisector of the angle. Be sure to leave all construction markings.
7. Find the perimeter and area of the figure. Label all side lengths. Show work!
P = ___________
A = ____________
8
4
548
7. Find the perimeter and area of the figure. Label all side lengths. Show work!
P = ___________
A = ____________
8
4
548
88 – 20
68
8. Examine the figure graphed on the axes at right.
a. What happens when you rotate this figure about the origin 45? 90? 180?
b. What other angles could the figure at right be rotated so that the shape does not appear to change?
It matches up
135, 225, 270, 315, 360
Scoring Your Homework
• Count how many problems you missed or didn’t do
• 0-1 missed = 10
• 2-3 missed = 9
• 4-5 missed = 8
• 6-7 missed = 7
• 8-9 missed = 6
• 10-11 missed = 5
• 12-13 missed = 4
• 14-15 missed = 3
• 16-17 missed = 2
• 18-19 missed = 1
• 20-21 missed = 0
2.2
What’s the Relationship?
Pg. 6Complementary, Supplementary, and Vertical Angles
2.2 – What's the Relationship?________________Complementary, Supplementary, and Vertical Angles
In Chapter 1, you compared shapes by looking at similarities between their parts. For example, two shapes might have sides of the same length or equal angles. In this chapter you will examine relationships between parts within a single shape or diagram. Today you will start by looking at angles to identify relationships in a diagram that make angle measures equal.
2.10 – ANGLE RELATIONSHIPSWhen you know two angles have a certain relationship, learning something about one of them tells you something about the other. Certain angle relationships come up often enough in geometry that we given them special names.
76
90 – 76 = 14
62
180 – 62 = 118
23
157
23
157
23
157
23
157CEB
AEC and DEB
54
126
54
126
b. Based on your observations, write a conjecture (a statement based on an educated guess that is unproven). Start with , "Vertical angles are ...“
Vertical angles are _________________.congruent
2.12 – PROVING VERTICAL ANGLES CONGRUENTThe last problem used what is called inductive reasoning to show that vertical angles are congruent. We are now going to start to use deductive reasoning to prove that all vertical angles are congruent, no matter what the angles measure. Below you are given the steps in order to prove that vertical angles are congruent. Your job is to explain why each statement is true. Match the reasons with the given statements.
A. Both add to 180B. Straight angles add to 180C. Subtract y from both sidesD. Straight angles add to 180
Straight angles add to 180
Straight angles add to 180
Both add to 180
Subtract y from both sides
90
40
50
40
2.14 –ANGLES RELATIONSHIPS
In the problems below, you will use geometric relationships to find angle measures. Start by finding a special relationship between some of the angles, and use that relationship to write an equation. Solve the equation for the variable, then use that variable to find the missing measurement.
Angle Relationship: __________________
Equation: __________________________
PNM = ____________________________
supplementary
x + 152 = 180 x = 28
28
28
Angle Relationship: __________________
Equation: __________________________
FGH = ____________________________
congruent
4x – 5 = 3x + 2 x = 7
23
23
Angle Relationship: __________________
Equation: __________________________
DBC = ____________________________
complementary
3x + 3 = 90 x = 29
36
36
Angle Relationship: __________________
Equation: __________________________
QPM = ____________________________
supplementary
2x + 28 = 180 x = 76
76
76
2.15 – SUMMARYDiscuss each different type of angle measurement: right, complementary, straight, supplementary, congruent, and vertical. What is their relationship? Are they equal or add to something? Draw a picture of each.
Right Complementary
One 90 angle Angles that add to 90
Straight Supplementary
One 180 angle Angles that add to 180
Congruent Vertical
Angles with same degree
Opposite angles that are congruent
P
Q R
S 12
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