In this example, the vertical angles are: Vertical Angles are two angles that are opposite each other when two lines intersect. a b c d In this example, the vertical angles are: Vertical angles have the same measurement. So:
Using what you know about vertical angles, find the measure of the missing angles. By Supplementary Angles: By Vertical Angles:
Are angles 2 and 4 vertical angles? 30 Are angles 2 and 4 vertical angles? A Yes 1 2 3 4 B No Answer: A Yes
Are angles 2 and 3 vertical angles? 31 Are angles 2 and 3 vertical angles? A Yes B No 1 2 3 4 Answer: B No
32 If angle 1 is 60 degrees, what is the measure of angle 3? You must be able to explain why. 2 1 3 4 Answer: 60 m3 = 60 Vertical angles
33 If angle 1 is 60 degrees, what is the measure of angle 2? You must be able to explain why. 2 1 3 4 Answer: 120 m2 = 180 - 60 m2 = 120 Supplementary
ABC is adjacent to CBD How do you know? Adjacent Angles are two angles that are next to each other and have a common ray between them. This means that they are on the same plane and they share no internal points. A B C D ABC is adjacent to CBD How do you know? ·They have a common side (ray CB) ·They have a common vertex (point B)
Adjacent or Not Adjacent? You Decide! b a b a b click to reveal Adjacent click to reveal Not Adjacent click to reveal Not Adjacent
Which two angles are adjacent to each other? 34 Which two angles are adjacent to each other? A 1 and 4 B 2 and 4 1 4 6 5 2 3 Answer: A
Which two angles are adjacent to each other? 35 Which two angles are adjacent to each other? A 3 and 6 B 5 and 4 2 1 4 5 3 6 Answer: A
Interactive Activity-Click Here A transversal is a line that cuts across two or more (usually parallel) lines. A P Q R B E F Interactive Activity-Click Here
In this diagram the corresponding angles are: Corresponding Angles are on the same side of the transversal and on the same side of the given lines. In this diagram the corresponding angles are: a b c d e f g h Transversal
Which are pairs of corresponding angles? 36 Which are pairs of corresponding angles? A 2 and 6 B 3 and 7 C 1 and 8 1 2 3 4 5 6 7 8 Answer: A, B
Which are pairs of corresponding angles? 37 Which are pairs of corresponding angles? A 2 and 6 B 3 and 1 6 3 C 1 and 8 2 5 4 1 8 7 Answer: B
Which are pairs of corresponding angles? 38 Which are pairs of corresponding angles? 1 2 A 1 and 5 3 4 B 2 and 8 5 6 C 4 and 8 7 8 Answer: A, C
A B C D E 39 Which pair of angles are not corresponding? 5 4 8 1 2 6 7 Answer: D
In this diagram the alternate exterior angles are: Alternate Exterior Angles are on opposite sides of the transversal and on the outside of the given lines. a b c d e f g h l In this diagram the alternate exterior angles are: m n Which line is the transversal?
In this diagram the alternate interior angles are: Alternate Interior Angles are on opposite sides of the transversal and on the inside of the given lines. In this diagram the alternate interior angles are: a b c d e f g h l m n
In this diagram the same side interior angles are: Same Side Interior Angles are on same sides of the transversal and on the inside of the given lines. In this diagram the same side interior angles are: a b c d e f g h l m n
A Yes B No 40 Are angles 2 and 7 alternate exterior angles? 1 3 5 7 2 6 8 m n l B No Answer: B No
Are angles 3 and 6 alternate exterior angles? 41 Are angles 3 and 6 alternate exterior angles? A Yes B No 1 3 5 7 2 4 6 8 m n l Answer: A Yes
Are angles 7 and 4 alternate exterior angles? 42 Are angles 7 and 4 alternate exterior angles? A Yes 1 3 5 7 2 4 6 8 m n l B No Answer: B No
Which angle corresponds to angle 5? A 3 B 4 C 2 D 6 43 Which angle corresponds to angle 5? A 3 B 4 1 3 5 7 2 4 6 8 m n l C 2 D 6 Answer: D
Which pair of angles are same side interior? 44 Which pair of angles are same side interior? A 3, 4 B 4, 7 1 3 5 7 2 4 6 8 m n l C 2, 4 D 6, 1 Answer: B
What type of angles are 3 and 6? 45 What type of angles are 3 and 6? A Alternate Interior Angles B Alternate Exterior Angles C Corresponding Angles D Vertical Angles E Same Side Interior 1 3 5 7 2 4 6 8 m n l Answer: B
What type of angles are 5 and 2? 46 What type of angles are 5 and 2? A Alternate Interior Angles B Alternate Exterior Angles C Corresponding Angles D Vertical Angles E Same Side Interior 1 3 5 7 2 4 6 8 m n l Answer: E
What type of angles are 5 and 6? 47 What type of angles are 5 and 6? A Alternate Interior Angles B Alternate Exterior Angles C Corresponding Angles D Vertical Angles E Same Side Interior 1 3 5 7 2 4 6 8 m n l Answer: C
Are angles 5 and 2 alternate interior angles? 48 Are angles 5 and 2 alternate interior angles? A Yes B No 1 3 5 7 2 4 6 8 m n l Answer: B No
Are angles 5 and 7 alternate interior angles? 49 Are angles 5 and 7 alternate interior angles? A Yes B No 1 3 5 7 2 4 6 8 m n l Answer: B No
Are angles 7 and 2 alternate interior angles? 50 Are angles 7 and 2 alternate interior angles? A Yes B No 1 3 5 7 2 4 6 8 m n l Answer: A Yes
Are angles 3 and 6 alternate interior angles? 51 Are angles 3 and 6 alternate interior angles? A Yes B No 1 3 5 7 2 4 6 8 m n l Answer: B No
Special Case!!! If parallel lines are cut by a transversal then: ·Corresponding Angles are congruent ·Alternate Interior Angles are congruent ·Alternate Exterior Angles are congruent SO: n 1 3 5 7 2 4 6 8 m l
52 Given the measure of one angle, find the measures of as many angles as possible. Which angles are congruent to the given angle? Type one answer into your responder. 4 5 6 2 7 1 8 l m n Answer: Angles 5, 7, and 1
What are the measures of the remaining angles? 53 Given the measure of one angle, find the measures of as many angles as possible. What are the measures of the remaining angles? 4 5 6 2 7 1 8 l m n Answer: 130 m4 + 50 = 180 m4 = 130
54 Given the measure of one angle, find the measures of as many angles as possible. Which angles are congruent to the given angle? Type one of the angles into the responder. l m 1 3 Answer: Angle 4 5 7 2 4 n 8
What are the measures of the remaining angles? 55 Given the measure of one angle, find the measures of as many angles as possible. What are the measures of the remaining angles? l m 1 3 Answer: m2 + 35 = 180 m2 = 145 m2 = m8 m8 = 145 5 7 2 4 n 8