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