Embed Size (px)
DESCRIPTION
8.3 Angle Relationships. 1. 2. Angle Relationships. Adjacent angles have a common vertex and a common side, but no common interior points. (They’re NEXT to each other and NOT necessarily supplementary). Writing Math. ~. The symbol for congruence is =, which is read as “is congruent to.”. - PowerPoint PPT Presentation
Citation preview
8.3 AngleRelationships
Angle Relationships
Adjacent angles have a common vertex and a common side, but no common interior points. (They’re NEXT to each other and NOT necessarily supplementary)
1 2
1 2is adjacent to
Finding Angle Measures
Use the diagram to find each angle measure.
A. If m1 = 37°, find m3.
1 and 2 are supplementary.
The measures of 2 and 3 are supplementary.
m2 = 180° – 37° = 143°
m3 = 180° – 143° = 37°
So m1 = m3, or 1 3.
The symbol for congruence is =, which is read as “is congruent to.”
Writing Math ~
Parallel and Perpendicular Lines
Intersecting Lines form Two Pair of Congruent Vertical Angles
12
34
1 3
2 4
Vertical angles are the nonadjacent angles formed by two intersecting lines. (They’re OPPOSITE each other).
3 5 4 6and
Alternate Interior Angles:
Opposite side of the transversal
Inside the parallel lines
5 6
4 3
1 2
8 7
A transversal is a line that intersects two or more lines that lie in the same plane.
Transversals to parallel lines form angle pairs with special properties.
Alternate Exterior Angles:
Opposite side of the transversal
Outside the parallel lines
1 7 2 8and
8
21
7
3 4
5 6
Corresponding Angles:
Same side of the transversal
One inside and one outside the parallel
lines
8
4
5
1 2
6
3
7
1 5 2 6and 3 7 4 8and
Vertical Angles:
Non-adjacent angles
(Angles across from each other)
1 3 2 4and 5 7 6 8and
8
4
5
1 2
6
3
7
Vertical
Supplementary Angles:
Angles that add to
180 degrees
1 2 ; 2 3 ; 3 4 ; 4 1and and and and
8
4
5
1 2
6
3
7
Supplementary
5 6 ; 6 7 ; 7 8 ; 8 5and and and and
In the figure, line l || line m. Find the measure of the angle.
Finding Angle Measures of Parallel Lines
Cut by Transversals
A.4
m4 = 124°
Corresponding angles are congruent.
Check It Out!
A.7
m7 = 144°
1 144°3 4
5 67 8
m
n
In the figure, line l || line m. Find the measure of the angle.
Alternate exterior angles are congruent.
B.1
m1 + 144° = 180°
1 is supplementary to the 144° angle.
m1 = 36°–144° –144° 1 144°
3 45 6
7 8
m
n
Check It Out!
In the figure, line l || line m. Find the measure of the angle.
