Adjacent, Vertical, Supplementary, and Complementary Angles Linear Pair, Perpendicular Lines

Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º

Vertical angles are opposite from one another. 75º 105º 105º 75º

Vertical angles are opposite from one another. 75º 105º 105º 75º

Vertical angles are congruent (equal). 150º 30º 150º 30º

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

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

Perpendicular Lines: intersect to form four right angles

Practice Time!

Practice Directions: Identify each pair of angles as vertical, supplementary, complementary, linear pair or none of the above.

#1 120º 60º

#1 120º 60º Supplementary Angles Linear Pair

#2 60º 30º

#2 60º 30º Complementary Angles

#3 75º 75º

#3 Vertical Angles 75º 75º

#4 60º 40º

#4 60º 40º None of the above

#5 60º 60º

#5 60º 60º Vertical Angles

#6 135º 45º

#6 135º 45º Supplementary Angles Linear Pair

#7 25º 65º

#7 25º 65º Complementary Angles

#8 90º 50º

#8 90º 50º None of the above

Directions: Determine the missing angle.

#1 ?º 45º

#1 135º 45º

#2 ?º 65º

#2 25º 65º

#3 ?º 35º

#3 35º 35º

#4 ?º 50º

#4 130º 50º

#5 ?º 140º

#5 140º 140º

#6 ?º 40º

#6 50º 40º

Angle Relationship: Investigation 1 The Linear Pair Conjecture 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:

Angle Relationship: Investigation 2 Vertical Angles Conjectures 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?

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.

Adjacent Practice: Vertical Complementary Supplementary Angle Addition Complete Angles Relationships Complete Angle Addition Quiz will be tomorrow Study guide tomorrow Test will be on Friday Complementary Supplementary Angle Addition Postulate Linear Pair

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 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 2. (5x + 18)º (7x + 12)º

Warm-Up: Find x and each measure 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 3. If m < IBT is 135, find <SBT. C 1 2 S 3 4 T How to measure and construct angles? How to analyze and measure pairs of angles? 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

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? Before Test Check study guide Any last minute questions before test