vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal...
TRANSCRIPT
Vocabulary
perpendicular linesparallel linesskew linesadjacent anglesvertical anglestransversalcorresponding angles
Insert Lesson Title Here
Course 2
8-3 Angle Relationships
When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines are equal to 90°, the lines are perpendicular lines.
Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel.
Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.
Course 2
8-3 Angle Relationships
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1A: Identifying Parallel, Perpendicular, and Skew Lines
The lines appear to intersect to form right angles.
UV and YV
UV YV
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1B: Identifying Parallel, Perpendicular, and Skew Lines
The lines are in different planes and do not intersect.
XU and WZ
XU and WZ are skew.
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1C: Identifying Parallel, Perpendicular, and Skew Lines
The lines are in the same plane and do not intersect.
XY and WZ
XY || WZ
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel, perpendicular, or skew.
Check It Out: Example 1A
The lines appear to intersect to form right angles.
WX and XUWX XU
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel, perpendicular, or skew.
Check It Out: Example 1B
The lines are in different planes and do not intersect.
WX and UV
WX and UV are skew
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel, perpendicular, or skew.
Check It Out: Example 1C
The lines are in the same plane and do not intersect.
WX and ZY
WX || ZY
Course 2
8-3 Angle Relationships
Course 2
8-3 Angle Relationships
Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementaryVertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
Reading Math
Course 2
8-3 Angle Relationships
A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed.
Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent.
Course 2
8-3 Angle Relationships
Line n line p. Find the measure of the angle.
Additional Example 2A: Using Angle Relationships to Find Angle Measures
22 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.
Course 2
8-3 Angle Relationships
Line n line p. Find the measure of the angle.
Additional Example 2B: Using Angle Relationships to Find Angle Measures
33 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m3 = 50°.
Course 2
8-3 Angle Relationships
Line n line p. Find the measure of the angle.
Additional Example 2C: Using Angle Relationships to Find Angle Measures
4
4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m4 = 130°.
Course 2
8-3 Angle Relationships
Line n line p. Find the measure of the angle.
Check It Out: Example 2A
3
3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°.
45°2 3 135°
5 647
n p
Course 2
8-3 Angle Relationships
Line n line p. Find the measure of the angle.
Check It Out: Example 2B
66 and the 135° angle are obtuse angles. Since vertical angles are congruent, m6 = 135°.
45°2 3 135°
5 647
n p
Course 2
8-3 Angle Relationships
Line n line p. Find the measure of the angle.
Check It Out: Example 2C
4
4 is an obtuse angle.
m4 + 45° = 180°–45° –45°
m4 = 135°
In the figure, the acute and obtuse angles are supplementary.Subtract 45° to isolate m4.
45°2 3 135°
5 647
n p
Course 2
8-3 Angle Relationships
Lesson Quiz
Tell whether the lines appear parallel, perpendicular, or skew.
1. AB and CD
2. EF and FH
3. AB and CG
4.
perpendicular
parallel
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skew
55°, 125°, 125°
In Exercise 28, line r line 5. Find the measure of 4, 5, and 6.
Course 2
8-3 Angle Relationships