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Name LESSON 3-2 Date Class Practice B Angles Formed by Parallel Lines and Transversals Find each angle measure. 2 133° 119° 1 47 1. m1 119 2. m2 # X ! (8X 34)° $ " (5X 2)° % & 97 3. mABC 62 4. mDEF Complete the two-column proof to show that same-side exterior angles are supplementary. 5. Given: p q Prove: m1 m3 180 Proof: 1 2 3 P Q Statements 1. p q 2. a. Reasons 1. Given m⬔2 m⬔3 180 3. 1 2 4. c. m⬔1 m⬔2 5. d. m⬔1 m⬔3 180 2. Lin. Pair Thm. 3. b. Corr. ⭄ Post. 4. Def. of 5. e. Subst. 6. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy’s wake as a line. m1 (2x 2y) and m2 (2x + y). Find x and y. x= 15 y= 40 Copyright © by Holt, Rinehart and Winston. All rights reserved. 1 12 2 70° Holt Geometry Name Date Class Name Practice A LESSON 3-2 LESSON 3-2 Angles Formed by Parallel Lines and Transversals 1. The Corresponding Angles Postulate states that if two parallel lines are cut by a Practice B Angles Formed by Parallel Lines and Transversals . 2 133° equal 2. Congruent angles have 47� 1. m�1 70° 1 119° 1 measures. Find each angle measure. 119� 2. m�2 2 � 140° �� � ��� 140� 3. m�1 Class Find each angle measure. congruent transversal, then the pairs of corresponding angles are Date � � (8� � 34)° 70� 4. m�2 � (5� � 2)° � 97� 3. m�ABC 62� 4. m�DEF Find x. 5. 6. (� � 15)° Complete the two-column proof to show that same-side exterior angles are supplementary. 120° 90° (� � 30)° 5. Given: p � q Prove: m�1 � m�3 � 180� 75 150 Proof: transversal parallel lines are cut by a 7. If two then the two pairs of alternate interior angles are congruent. , 10. alternate interior angles 4. c. 5. d. m�1 � m�3 � 180� �1 and �7; �2 and �8 2 1 3 4 6 5 7 8 12. same-side interior angles �3 and �6; �4 and �5 11 Copyright © by Holt, Rinehart and Winston. All rights reserved. Name Date Class Holt Geometry x= 15 y= 40 LESSON 1. A parallelogram is a quadrilateral formed by two pairs of parallel lines. Use what you know about parallel lines and angle measures to find the sum of the measures of the four angles inside the parallelogram. Explain your answer. 3-2 Angles Formed by Parallel Lines and Transversals � � 2 1 �1 � �3 4 Determine whether each pair of angles is congruent according to the Corresponding Angles Postulate. � 3� � 2 � 1 4 1. �1 and �2 Reasons 1. Construction 2. Same-Side Int. � Thm. 3. Add. Prop. of � 4. m�3 � m�CEB � m�CBE � 180� 4. Given 5. m�DEB � m�CEB � 180� 5. Lin. Pair Thm. 6. Subst. (Steps 4, 5) 9. m�2 � m�ABE � m�CBE 13 Copyright © by Holt, Rinehart and Winston. All rights reserved. 4 2 � Statements ‹___› 1. Draw BE parallel to AD. 2. m�1 � m�ABE � 180�, m�4 � m�DEB � 180� 3. m�1 � m�4 � m�ABE � m�DEB � 360� 10. m�1 � m�2 � m�3 � m�4 � 360� 3 1 360°; sample answer: 7. m�3 � m�CBE � m�DEB 8. m�1 � m�3 � m�4 � m�ABE � m�CBE � 360� �2 � �4 � 3 Given: The sum of the measures of the angles in a triangle is 180�. 6. m�3 � m�CEB � m�CBE � m�DEB � m�CEB Holt Geometry � Same-Side Int. � Thm. Thus, the total of the angle measures is 360°. _ Class Reteach Sample answer: m�1 � m�2 � 180° and m�3 � m�4 � 180° by the 3. A trapezium is a quadrilateral formed by four lines, no two of which are parallel. Find the sum of the measures of the four angles inside the trapezium. Write proof _ a two-column ‹__› to justify your‹___ answer. (Hint: Draw BE parallel to AD and › having E on CD. Write Construction to justify this step.) Date 4 1 2. A trapezoid is a quadrilateral formed by one pair of parallel lines. Use what you know about parallel lines and angle measures to find the sum of the measures of the four 360° angles inside the trapezoid. 70° 2 1 According to the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3 2 12 Name Angles Formed by Parallel Lines and Transversals Copyright © by Holt, Rinehart and Winston. All rights reserved. Subst. 5. e. Copyright © by Holt, Rinehart and Winston. All rights reserved. Practice C Prove: m�1 � m�2 � m�3 � m�4 � 4. Def. of � � 6. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy’s wake as a line. m�1 � (2x � 2y)� and m�2 � (2x + y)�. Find x and y. 11. alternate exterior angles �3 and �5; �4 and �6 3-2 Corr. � Post. 3. b. m�1 � m�2 . Give two examples of each kind of angle pair in the figure. LESSON 2. Lin. Pair Thm. 3. �1 � �2 . congruent 1. Given m�2 � m�3 � 180� 2. a. 9. If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are Reasons 1. p � q 8. If two parallel lines are cut by a transversal, then the two pairs of same-side supplementary 2 3 � Statements Fill in the blanks to complete these theorems about angle pairs. interior angles are 1 � 2. �3 and �4 no yes Find each angle measure. 1 �° � 67° � � 142° 3. m�1 4. m�HJK 67° 7. Subtr. Prop. of � 8. Subst. (Steps 3, 7) ���������� 142° � �� � � �� � � � 5. m�ABC 9. Angle Add. Post. 10. Subst. (Steps 8, 9) Copyright © by Holt, Rinehart and Winston. All rights reserved. 53 � 6. m�MPQ 92° Holt Geometry � ���������� � � 125° 14 Holt Geometry Holt Geometry