Vocabulary
Any line that intersects two or more coplanar lines.
transversal
If two parallel lines are cut by a transversal, these angles are on the inside of the two parallel lines and on the same side of the transversal.
Same Side Interior Angles (Consecutive Interior)
Two angles are congruent. The measure of the first angles is 42°, what is the measure of the second angle
42°
If a pair of adjacent angles formed by an intersecting line are linear pairs, what is their relationship?
supplementary
If a transversal cuts two parallel lines, how many angle measures do you need to know to figure out all 8 angle measures in the figure.
1
Two angles whose measures add up to 180°
supplementary angles
Two angles whose measures add up to 90o
Complementary Angles
What is the relationship between angles 4 and 5?
Alternate Interior Angles.
One way to prove that lines are parallel lines is through understanding that corresponding angles are _________?
congruent
If the measure of <4 is 62° and the measure of <6 is 4x, what is the value of x and what is the measure of <7?
62 + 4x = 180
4x = 118
x=29.5 ; 4(29.5)= 118 <7 = 118°
When 2 parallel lines, l and m, are both intersected by a transversal, these angles occupy the same position on the 2 parallel lines.
Corresponding Angles.
A pair of adjacent angles formed by intersecting lines.
Linear Pair Angles.
If the measure of angle 8 is 112°, what is the measure of angle 6?
68°
To prove that lines are parallel one must understand that same side (Consecutive) interior angles are _________.
supplementary
If the measure of <1 is 4x-6 and the measure of <8 is 122°, what is the value of x?
4x-6=122 x=32
Congruent angles formed by two intersecting lines
Vertical Angles.
If two parallel lines are intersected by a transversal these angles are located on the outside of the two parallel lines and on the same side of the transversal.
Same Side Exterior Angles (Consecutive Exterior).
What is the relationship between angles 1 and 4?
Vertical Angles.
If the measure of angle 2 is 30°, what is the measure of angle 7?
30°
If the measure of <3 is 150° and the measure of <6 is 3x, what is the value of x and what is the measure of <7?
<7=150°; and 3x=150 x=50
When 2 parallel lines are both intersected by a transversal these angles are inside of the two parallel lines and on opposite sides of the transversal.
Alternate Interior Angles.
Coplanar lines that do not intersect.
What are parallel lines.
If the measure of angle 1 is 37°, what is the measure of angle 8 and what is the angle relationship?
37°; Alternate Exterior
Given that l || m, m<1=98°, then the measures of <3 and <8 are:
82° and 98°
If the measure of <4 is 8x+35 and the measure of <6 is 2x+5, then find the value of x and find the measure of <8?
8x+35+2x+5=180
10x+40=180
10x=140
x=14
Now plug into <4 because it is congruent (corresponding) to <8.
8(14)+35=147 so <8=147°