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### 2.2 side lengths. Show work!

1. Estimate the size of each angle below. Then determine if it is acute, right, obtuse, or straight.

180

170

90

100

30

- Find the measure of the following angles: it is acute, right, obtuse, or straight.
- EDF = ___________
- ADE = ___________
- CDF = ___________
- d. FDC = ___________

35

145

100

100

3. Complete the statements based on the markings in the picture.

MJI

- LJK___________
- LMP___________
- c. JIH___________

GHQ

PIG

- In the picture, picture.mMRT = 133.
- Is MRT acute, right or obtuse?
- 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!

8

48

P = ___________

A = ____________

5

4

7. Find the perimeter and area of the figure. Label all side lengths. Show work!

8

48

P = ___________

A = ____________

5

68

4

88 –

20

- Examine the figure graphed on side lengths. Show work!
- the axes at right.
- What happens when you rotate this figure about the origin 45? 90? 180?
- 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 side lengths. Show work!

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

What’s the Relationship?

Pg. 6

Complementary, Supplementary, and Vertical Angles

2.2 – What's the Relationship?________________ side lengths. Show work!

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 RELATIONSHIPS side lengths. Show work!

When 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.

AEC and DEB side lengths. Show work!

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 CONGRUENT statement based on an educated guess that is unproven). Start with , "

The 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 180 statement based on an educated guess that is unproven). Start with , "

B. Straight angles add to 180

C. Subtract y from both sides

D. Straight angles add to 180

Straight angles add to 180

Straight angles add to 180

Both add to 180

Subtract y from both sides

2.14 –ANGLES RELATIONSHIPS statement based on an educated guess that is unproven). Start with , "

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.

28 statement based on an educated guess that is unproven). Start with , "

supplementary

Angle Relationship: __________________

Equation: __________________________

PNM = ____________________________

x = 28

x + 152 = 180

28

23 statement based on an educated guess that is unproven). Start with , "

congruent

Angle Relationship: __________________

Equation: __________________________

FGH = ____________________________

x = 7

4x – 5 = 3x + 2

23

36 statement based on an educated guess that is unproven). Start with , "

complementary

Angle Relationship: __________________

Equation: __________________________

DBC = ____________________________

x = 29

3x + 3 = 90

36

76 statement based on an educated guess that is unproven). Start with , "

supplementary

Angle Relationship: __________________

Equation: __________________________

QPM = ____________________________

x = 76

2x + 28 = 180

76

2.15 – SUMMARY statement based on an educated guess that is unproven). Start with , "

Discuss 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.

Angles that add to 90 statement based on an educated guess that is unproven). Start with , "

One 90 angle

Angles that add to 180 statement based on an educated guess that is unproven). Start with , "

One 180 angle

P statement based on an educated guess that is unproven). Start with , "

S

1

2

Q

R

Opposite angles that are congruent

Angles with same degree

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