3-2 Angles Formed By Parallel Lines
AnglesFormedby ParallelLinesAnglesFormedbyParallel3-23-2 and Transversalsand TransversalsWarm UpLesson PresentationLesson QuizHoltGeometryHoltMcDougalGeometryLines
3-2Angles Formed by Parallel Linesand TransversalsWarm UpIdentify each angle pair.1. 1 and 3corr. s2. 3 and 6alt. int. s3. 4 and 5alt. ext. s4. 6 and 7same-side int sHolt McDougal Geometry
3-2Angles Formed by Parallel Linesand TransversalsObjectiveProve and use theorems about theangles formed by parallel lines and atransversal.Holt McDougal Geometry
3-2Angles Formed by Parallel Linesand TransversalsHolt McDougal Geometry
3-2Angles Formed by Parallel Linesand TransversalsExample 1: Using the Corresponding AnglesPostulateFind each angle measure.A. m ECFx 70 Corr. s Post.m ECF 70 B. m DCE5x 4x 22x 22m DCE 5x 5(22) 110 Holt McDougal GeometryCorr. s Post.Subtract 4x from both sides.Substitute 22 for x.
3-2Angles Formed by Parallel Linesand TransversalsCheck It Out! Example 1Find m QRS.x 118 Corr. s Post.m QRS x 180 m QRS 180 – xDef. of Linear PairSubtract x from both sides. 180 – 118 Substitute 118 for x. 62 Holt McDougal Geometry
3-2Angles Formed by Parallel Linesand TransversalsExample 2: Finding Angle MeasuresFind each angle measure.A. m EDGm EDG 75 Alt. Ext. s Thm.B. m BDGx – 30 75 Alt. Ext. s Thm.x 105 Add 30 to both sides.m BDG 105 Holt McDougal Geometry
3-2Angles Formed by Parallel Linesand TransversalsCheck It Out! Example 2Find m ABD.2x 10 3x – 15 Alt. Int. s Thm.x 25Subtract 2x and add 15 toboth sides.m ABD 2(25) 10 60 Substitute 25 for x.Holt McDougal Geometry
3-2Angles Formed by Parallel Linesand TransversalsLesson QuizState the theorem or postulate that is relatedto the measures of the angles in each pair.Then find the unknown angle measures.1. m 1 120 , m 2 (60x) Alt. Ext. s Thm.; m 2 120 2. m 2 (75x – 30) ,m 3 (30x 60) Corr. s Post.; m 2 120 ,m 3 120 3. m 3 (50x 20) , m 4 (100x – 80) Alt. Int. s Thm.; m 3 120 , m 4 120 4. m 3 (45x 30) , m 5 (25x 10) Same-Side Int. s Thm.; m 3 120 , m 5 60 Holt McDougal Geometry
3-2 Angles Formed by Parallel Lines and Transversals Lesson Quiz State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m 1 120 , m 2 (60x) 2. m 2 (75x –30) , m 3 (30x 60) Corr. s Post.; m 2 120 , m 3 120 Alt. Ext. s Thm.; m 2
- Page 8 Measuring Angles: Real-Life Objects - Page 9 Draw Angles - Page 10 Draw Angles: More Practice - Page 11 Put It All Together: Measure & Draw Angles - Page 12 Joining Angles - Page 13 Joining More Than Two Angles - Page 14 More Practice: Joining Angles - Page 15 Separating Angles .
Adjacent angles are two angles that share a common vertex and side, but have no common interior points. 5 and 6 are adjacent angles 7 and 8 are nonadjacent angles. Notes: Linear Pairs and Vertical Angles Two adjacent angles are a linear pair when Two angles are vertical angles when their noncommon sides are opposite rays.
two acute vertical angles 62/87,21 Vertical angles are two nonadjacent angles formed by two intersecting lines. You can use the corner of a piece of paper to see that Ø ZVY and Ø WVU are less than right angles. 7KHUHIRUH DQG DUHDFXWHYHUWLFDO angles. two obtuse adjacent angles 62/87,21 Adjacent angles are two angles that lie in the same
Vertical Angles Words Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent. Examples 4 2 3 1 1 and 3 are vertical angles. 2 and 4 are vertical angles. EXAMPLE 2 Finding Angle Measures Find the value of x. a. 70 x The
two acute vertical angles . Geometry Unit 2 Note Sheets (Segments, Lines & Angles) 6 Angle Pair Relationships Vertical Angles Complementary Angles Supplementary Angles Linear Pair Guided Practice 5. Find the measures of two supplementary angles if the measures of one angles is 6 less than five t
vertical angles. Vertical angles have the same measure. Vertical angles are also called opposite angles. 1 and 2 are vertical angles. 3 and 4 are vertical angles. 14. In this triangle, name a pair of complementary angles. m T 30 m L 60 30 60 90 . So T and L are complementary angles. 15. In this parallelogram, name a pair of .
Adjacent Angles: Two angles and with a common side ⃗⃗⃗⃗⃗ are adjacent angles if belongs to the interior of . Vertical Angles: Two angles are vertical angles (or vertically opposite angles) if their sides form two pairs of opposite rays. Angles on a Line: The sum of the me
Sort the following angles into pairs of complementary angles (two angles that have measures that add up to 900) and supplementary angles (two angles that have measures that add up to 180 0 ). WAM 10 Ch.5: Angles & Parallel Lines Extra Notes Handout Page 5
