ADJACENT, VERTICAL, SUPPLEMENTARY, AND COMPLEMENTARY ANGLESLINEAR PAIR, PERPENDICULAR LINES

Adjacent angles are “side by side” and share a common ray.

45º15º

These are examples of adjacent angles.

55º

35º

50º130º

80º 45º

85º20º

These angles are NOT adjacent.

45º55º

50º100º

35º

35º

When 2 lines intersect, they make vertical angles.

75º

75º

105º105º

Vertical angles are opposite from one another.

75º

75º

105º105º

Vertical angles are opposite from one another.

75º

75º

105º105º

Vertical angles are congruent (equal).

30º150º

150º30º

Supplementary angles add up to 180º.

60º120º

40º

140º

Adjacent and Supplementary Angles

Supplementary Anglesbut not Adjacent

Complementary angles add up to 90º.

60º

30º40º

50º

Adjacent and Complementary Angles

Complementary Anglesbut not Adjacent

Linear Pair: a pair of adjacent angles that measures 180°

Perpendicular Lines: intersect to form four right angles

Practice Time!

PracticeDirections: Identify each pair of angles as vertical, supplementary, complementary, linear pairor none of the above.

#1

60º120º

#1

60º120º

Supplementary Angles

Linear Pair

#2

60º30º

#2

60º30º

Complementary Angles

#3

75º75º

#3

75º75º

Vertical Angles

#4

60º40º

#4

60º40º

None of the above

#5

60º

60º

#5

60º

60º

Vertical Angles

#6

45º135º

#6

45º135º

Supplementary Angles

Linear Pair

#7

65º

25º

#7

65º

25º

Complementary Angles

#8

50º90º

#8

50º90º

None of the above

Directions:Determine the missing angle.

#1

45º?º

#1

45º135º

#2

65º

?º

#2

65º

25º

#3

35º

?º

#3

35º

35º

#4

50º

?º

#4

50º

130º

#5

140º

?º

#5

140º

140º

#6

40º

?º

#6

40º

50º

Angle Relationship: Investigation 1

Materials: paper, pencil, 2 sheets of patty paper & protractor

Draw line PQ and place a point R between P and Q.

Choose another point S not on line PQ and draw ray RS. You have just create a linear pair of angles.

Place the “zero edge” of your protractor along line PQ. What do you notice about the sum of the measures of the linear pair of angles?

Compare your results with those of your class. Does everyone make the same observation?

What is the Linear Pair Conjecture? Example:

The Linear Pair Conjecture

Angle Relationship: Investigation 2

Materials: paper, pencil, 2 sheets of patty paper & protractor

Fold patty paper, make a crease, outline the crease, place points A & B on the line.

Fold patty paper again so that you form intersecting lines, make a crease, outline the crease, place points D & E on the line and label the intersection C. (Make sure C is between A & B)

Which angles are vertical angles? Fold the paper again through point C so that

<ACD lies on top of <ECB. What do you notice? What do you notice about their measures?

Vertical Angles Conjectures

Angle Relationship Activity p. 54 Your Turn… Fold through C so that <ACE lies on DCB.

What do you notice? Compare your results with the class. What is the Vertical Angles Conjecture? Use a protractor to measure each

angles. Write the measures on drawing. Name the linear pairs. What do you

notice about their measures? Repeat this activity with another piece of

patty paper. What do you notice?

Practice: complementary and supplementary Let’s Race! Find a partner, get a deck of cards, and

play “Say it faster!” Whoever say the complement/supplement

faster gets the pair of cards. The person with the most cards, WINS! 10, Jacks, Queens, Kings, & Aces = 1 Every other find the complement or

supplement.

Practice:

Complete Angles Relationships Complete Angle Addition Quiz will be tomorrow Study guide tomorrow Test will be on Friday

Adjacent

Vertical

Complementary

Supplementary

Linear PairAngle Addition

Postulate

Warm-Up: Identify each pair of angles Use: adjacent, vertical, complementary, supplementary, and/or linear pair 1. <1 & <2

2. <1 & <4 2 3 1 3. <4 & <5 5 4

4. <3 & <4

Warm-Up: Find x and each measure 1. (5x+ 16)º

(6x + 8)º

2.

(5x + 18)º

(7x + 12)º

3. (10x + 35)º

(13x + 30)º

4. Ray BC is an angle bisector.

Find <CBD & <ABC. A

63º

B C

D

Warm-Up: Find x and each measure 1. (5x+ 16)º

(6x + 8)º

2.

(5x + 18)º

(7x + 12)º

Warm-Up: Find x and each measure

3. (10x + 35)º

(13x + 30)º

4. Ray BC is an angle bisector.

Find <CBD & ABC. A

63º

B C

D

Warm-Up: Angle Addition

1. The m < ABC = 6x – 8, m < ABD = 3x + 2, and m < DBC = 2x – 1. Find the measure of each angle.

A

B D

C

Warm-Up:

A I

C 1 2 S

3 4 T 1. Name angle 3.

2. < 3 & <4 are….

3. If m < IBT is 135, find <SBT.

4. <4 = 4x + 5 & <3 = 6x + 5. Find each measure.

B

How to measure and construct angles? How to analyze and measure pairs of angles?

Before Test

Check study guide

Any last minute questions before test

How to measure and construct angles? How to analyze and measure pairs of angles?