8 3 Line and Angle Relationships Warm Up

8 -3 Line and Angle Relationships Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

8 -3 Line and Angle Relationships Math Journal (5 Min) • 3 -2 -1 - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write 3 statements that they already know about the lesson being presented, 2 questions that they have before the lesson is presented, and 1 connection that they feel can be made between what they already know and what they think they will be taught in the new lesson before they have been taught the lesson, and at the end of class, write 3 statements that they now know about the lesson being presented, answer the 2 questions that they had written previously, and 1 connection that they now know can be made between what they knew before the lesson and what they now know after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 statement or connection that pertained to the lesson.

8 -3 Line and Angle Relationships Homework Review (5 Min)

8 -3 Line and Angle Relationships Warm Up Find the complement of each angle measure. 1. 30° 60° 2. 42° 48° Find the supplement of each angle measure. 3. 150° 30° 4. 82° 98°

8 -3 Line and Angle Relationships 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

8 -3 Line and Angle Relationships Textbook Examples (I Do) (5 Min)

8 -3 Line and Angle Relationships Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

8 -3 Line and Angle Relationships Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal

8 -3 Line and Angle Relationships 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.

8 -3 Line and Angle Relationships Reading Math The symbol means “is parallel to. ” The symbol means “is perpendicular to. ”

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

8 -3 Line and Angle Relationships Additional Example 1 B: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XU and WZ are skew. The lines are in different planes and do not intersect.

8 -3 Line and Angle Relationships Additional Example 1 C: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XY and WZ XY || WZ The lines are in the same plane and do not intersect.

8 -3 Line and Angle Relationships Check It Out: Example 1 A Tell whether the lines appear parallel, perpendicular, or skew. WX and XU WX XU The lines appear to intersect to form right angles.

8 -3 Line and Angle Relationships Check It Out: Example 1 B Tell whether the lines appear parallel, perpendicular, or skew. WX and UV are skew. The lines are in different planes and do not intersect.

8 -3 Line and Angle Relationships Check It Out: Example 1 C Tell whether the lines appear parallel, perpendicular, or skew. WX and ZY WX || ZY The lines are in the same plane and do not intersect.

8 -3 Line and 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 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.

8 -3 Line and Angle Relationships Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

8 -3 Line and Angle Relationships A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

8 -3 Line and Angle Relationships

8 -3 Line and Angle Relationships Additional Example 2 A: 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°.

8 -3 Line and Angle Relationships Additional Example 2 B: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 3 m 3 + 130° = 180° – 130° m 3 = 50° Adjacent angles formed by two intersecting lines are supplementary. Subtract 130° to isolate m 3.

8 -3 Line and Angle Relationships Additional Example 2 C: 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°.

8 -3 Line and Angle Relationships Check It Out: Example 2 A Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 3 n p 3 and the 45° angle are vertical angles. Since vertical angles are congruent, m 3 = 45°.

8 -3 Line and Angle Relationships Check It Out: Example 2 B Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 6 n p 6 and the 135° angle are vertical angles. m 6 = 135°.

8 -3 Line and Angle Relationships Check It Out: Example 2 C 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° Subtract 45° to isolate m 4 = 135°

8 -3 Line and Angle Relationships Class work Problems (We Do) (10 Min) • Pg. 324 -325 (1 -6)

8 -3 Line and Angle Relationships

8 -3 Line and Angle Relationships Small Group CW(Yall Do) (10 Min) • Pg. 324 -325 (8 -26 EOE)

8 -3 Line and Angle Relationships

8 -3 Line and Angle Relationships

8 -3 Line and Angle Relationships

8 -3 Line and Angle Relationships Homework (You Do) (10 Min) • Pg. 324 -325 (9, 11, 15, 17, 21 odd)

8 -3 Line and Angle Relationships Math Journal (5 Min) • 3 -2 -1 - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write 3 statements that they already know about the lesson being presented, 2 questions that they have before the lesson is presented, and 1 connection that they feel can be made between what they already know and what they think they will be taught in the new lesson before they have been taught the lesson, and at the end of class, write 3 statements that they now know about the lesson being presented, answer the 2 questions that they had written previously, and 1 connection that they now know can be made between what they knew before the lesson and what they now know after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 statement or connection that pertained to the lesson.

8 -3 Line and Angle Relationships Lesson Quizzes Standard Lesson Quiz for Student Response Systems

8 -3 Line and Angle Relationships Lesson Quiz Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD parallel 2. EF and FH perpendicular 3. AB and CG skew 4. In Exercise 28, line r || line s. Find the measures of 4, 5, and 7. 55°, 125°

8 -3 Line and Angle Relationships 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

8 -3 Line and Angle Relationships 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

8 -3 Line and Angle Relationships 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

8 -3 Line and Angle Relationships Lesson Quiz for Student Response Systems 4. In the figure, line x || line y. Identify the measures of 2, 6, and 7. A. 70°, 110°, 70° B. 110°, 70° C. 110°, 70° D. 70°, 110°