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Transcript
Name_____________________________________ Class____________________________ Date________________ Lesson 3-1 Properties of Parallel Lines Lesson Objectives 1 Identify angles formed by two lines and a transversal 2 Prove and use properties of parallel lines NAEP 2005 Strand: Measurement Topic: Measuring Physical Attributes Local Standards: ____________________________________ All rights reserved. Vocabulary and Key Concepts. Postulate 3-1: Corresponding Angles Postulate If a transversal intersects two parallel lines, then corresponding angles are . 1 2 / m Theorem 3-1: Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are . © Pearson Education, Inc., publishing as Pearson Prentice Hall. t a b t 4 3 2 1 5 6 Theorem 3-2: Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are . m1 m2 Theorem 3-3: Alternate Exterior Angles Theorem If a transversal intersects two parallel lines, then alternate exterior angles are . Theorem 3-4: Same-Side Exterior Angles Theorem If a transversal intersects two parallel lines, then same-side exterior angles are . m4 m6 Daily Notetaking Guide Geometry Lesson 3-1 49 Name_____________________________________ Class____________________________ Date ________________ A transversal is t 56 13 42 78 / m Alternate interior angles are Same-side interior angles are and are same-side interior angles. Corresponding angles are and corresponding angles. A two-column proof is a display that shows column shows All rights reserved. and are alternate interior angles. The first and the second column Examples. 1 Applying Properties of Parallel Lines In the diagram of Compare 2 and the angle vertical to 1. Classify the angles as alternate interior angles, same-side interior angles, or corresponding angles. 2 3 1 The angle vertical to 1 is between the runway segments. 2 is between the runway segments and on the opposite side of the transversal runway. Because are not adjacent and lie between the lines on opposite sides of the transversal, 2 and the angle vertical to 1 are 50 Geometry Lesson 3-1 . Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. Lafayette Regional Airport, the black segments are runways and the gray areas are taxiways and terminal buildings. Name_____________________________________ Class____________________________ Date ________________ p 2 Finding Measures of Angles In the diagram at right, m and pq. Find m1 and m2. 1 and the 42 angle are Because m, m1 q 8 6 7 2 1 3 . by the 4 5 . 42 / m Because 1 and 2 are adjacent angles that form a straight angle, m1 m2 If you substitute All rights reserved. . for m1, the equation becomes from each side to find m2 Subtract . / a b c In the diagram, m. Find the values of a, b, and c. a Theorem c Theorem b . 3 Using Algebra to Find Angle Measures abc © Pearson Education, Inc., publishing as Pearson Prentice Hall. by the 40 65 m Postulate Substitution Property of Equality b Subtraction Property of Equality Quick Check. 1. Use the diagram in Example 1. Classify 2 and 3 as alternate interior angles, same-side interior angles, or corresponding angles. 2. Using the diagram in Example 2 find the measure of each angle. Justify each answer. a. 3 b. 4 c. 5 d. 6 e. 7 f. 8 3. Find the values of x and y. Then find the measures of the four angles in the trapezoid. y° 2x° (y 50)° Daily Notetaking Guide Geometry Lesson 3-1 51