Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find the complement of each angle measure. 1. 30° 2. 42° 60° 48° Find the supplement of each angle measure. 3. 150° 30° 4. 82° 98°

Problem of the Day Draw three points that are not on the same line. Label them A, B, and C. How many lines can you draw that are determined by the points? Name the lines. 3; AB, AC, BC 3

Objective: TLWBAT calculate unknown angles by using facts about parallel/perpendicular lines and a transversal to correctly calculate at least 14 out of 17 missing angles. NJCCCS 4.2.7.A.1 Common Core 7.G.B.5

Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal

When lines, segments, or rays intersect, they form angles When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines measure 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.

The symbol means “is parallel to The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math

8-3 Additional Example 1A: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. UV and YV The lines appear to intersect to form right angles. UV  YV

Additional Example 1B: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XU and WZ The lines are in different planes and do not intersect. XU and WZ are skew.

Additional Example 1C: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XY and WZ The lines are in the same plane and do not intersect. XY || WZ

Check It Out: Example 1A Tell whether the lines appear parallel, perpendicular, or skew. WX and XU WX  XU The lines appear to intersect to form right angles.

Check It Out: Example 1B Tell whether the lines appear parallel, perpendicular, or skew. WX and UV The lines are in different planes and do not intersect. WX and UV are skew.

Check It Out: Example 1C Tell whether the lines appear parallel, perpendicular, or skew. WX and ZY The lines are in the same plane and do not intersect. WX || ZY

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 supplementary Vertical angles are the opposite angles formed by two intersecting lines. Angles 1 and 3 in the diagram are vertical angles. Vertical angles have the same measure, so they are congruent.

Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

A transversal is a line that intersects two or more lines A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

Additional Example 2A: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 2 2 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

Line n line p. Find the measure of the angle. Additional Example 2B: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 3 Adjacent angles formed by two intersecting lines are supplementary. m3 + 130° = 180° –130° –130° Subtract 130° to isolate m3. m3 = 50°

Additional Example 2C: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 4 Alternate interior angles are congruent. m4 = 130°.

Line n line p. Find the measure of the angle. Check It Out: Example 2A Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 n p 3 3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°.

Line n line p. Find the measure of the angle. Check It Out: Example 2B Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 n p 6 6 and the 135° angle are vertical angles. m6 = 135°.

Line n line p. Find the measure of the angle. Check It Out: Example 2C Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 4 n p Adjacent angles formed by two intersecting lines are supplementary. m4 + 45° = 180° –45° –45° Subtract 45° to isolate m4. m4 = 135°

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Tell whether the lines appear parallel, perpendicular, or skew. Lesson Quiz Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD 2. EF and FH 3. AB and CG 4. parallel perpendicular skew In Exercise 28, line r || line s. Find the measures of 4, 5, and 7. 55°, 125°, 125° 25

Lesson Quiz for Student Response Systems 1. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none

Lesson Quiz for Student Response Systems 2. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none

Lesson Quiz for Student Response Systems 3. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none

EXIT TICKET In the figure, line x || line y. Identify the measures of 2, 6, and 7. A. 70°, 110°, 70° B. 110°, 70°, 70° C. 110°, 110°, 70° D. 70°, 70°, 110°