mcc8.g.5 angles and parallel lines intersecting lines lines that cross at exactly one point
TRANSCRIPT
MCC8.G.5
Angles and Parallel Lines
Intersecting Lines
• Lines that cross at exactly one point.
Perpendicular Lines
• Lines that intersect to form right angles.
PARALLEL LINES
• Def: line that do not intersect.
• Illustration:
• Notation: l || m AB || CD
lm
A
B
C
D
Examples of Parallel Lines
• Hardwood Floor
• Opposite sides of windows, desks, etc.
• Parking slots in parking lot
• Parallel Parking
• Streets
Examples of Parallel Lines
• Streets: Belmont & School
Transversal
• Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
tm
n
Vertical Angles & Linear Pair
Vertical Angles:
Linear Pair:
1 4, 2 3, 5 8, 6 7
Two angles that are opposite angles. Vertical angles are congruent.
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
Supplementary angles that form a line (sum = 180)
1 23 4
5 6
7 8
Supplementary Angles/Linear Pair
• Two angles that form a line (sum=180)
1 2
3 4
5 6
7 8
t
5+6=1806+8=1808+7=1807+5=180
1+2=1802+4=1804+3=1803+1=180
Supplementary Angles/Linear Pair
• Find the measures of the missing angles
? 72
?
t
108
108 180 - 72
Complementary Angles
• Two angles whose measures add to 90˚.
Adjacent Angles
• Angles in the same plane that have a common vertex and a common side.
Angles and Parallel Lines
• If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.
1. Corresponding angles
2. Alternate interior angles
3. Alternate exterior angles
• If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.
1. Consecutive interior angles
2. Consecutive exterior angles Continued…..
Corresponding Angles
Corresponding Angles: Two angles that occupy corresponding positions.
2 6, 1 5, 3 7, 4 8
1 2
3 4
5 6
7 8
Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.
Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º
m1 +m7 = 180º, m2 +m8 = 180º
1 23 4
5 6
7 8
Alternate Angles
• Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair).
• Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.
3 6, 4 5
2 7, 1 8
1 2
3 4
5 6
7 8
Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles
when m< 1 = 100°. Justify your answers.
m<2=80° m<3=100° m<4=80°
m<5=100° m<6=80° m<7=100° m<8=80°
m<9=100° m<10=80° m<11=100° m<12=80°
m<13=100° m<14=80° m<15=100° m<16=80°
t
16 15
1413
12 11
109
8 7
65
34
21
s
DC
BA
Example:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
If line AB is parallel to line CD and s is parallel to t, find:
2. the value of x, if m<1 = 100 and m<8 = 2x + 10.
3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.
ANSWERS:
t
16 151413
12 11
109
8 7
65
34
21
s
DC
BA
1. 30
2. 35
3. 33