3.2 Use Parallel Lines and
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1 3. Use Parallel Lines and Transversals Goal Use angles formed by arallel lines and ransversals. Your Noes POSTULATE CORRESPONDING ANGLES POSTULATE If wo arallel lines are cu by a ransversal, hen he airs of corresonding angles are. Examle The measure of hree of he numbered angles is. Idenify he angles. Exlain your reasoning. Soluion Idenify congruen angles By he Corresonding Angles Posulae,. Using he Verical Angles Congruence Theorem,. 7 Because and are corresonding angles, by he, you know ha. Checkoin Comlee he following exercise using he diagram shown.. If m 7 7, find m, m 3, and m. Tell which osulae or heorem you use in each case. 3 7 Lesson 3. Geomery Noeaking Guide Coyrigh Hol McDougal. All righs reserved.
2 3. Use Parallel Lines and Transversals Goal Use angles formed by arallel lines and ransversals. Your Noes POSTULATE CORRESPONDING ANGLES POSTULATE If wo arallel lines are cu by a ransversal, hen he airs of corresonding angles are congruen. Examle The measure of hree of he numbered angles is. Idenify he angles. Exlain your reasoning. Soluion Idenify congruen angles By he Corresonding Angles Posulae, m 7. Using he Verical Angles Congruence Theorem, m. 7 Because and are corresonding angles, by he Corresonding Angles Posulae, you know ha m. Checkoin Comlee he following exercise using he diagram shown.. If m 7 7, find m, m 3, and m. Tell which osulae or heorem you use in each case. m 3 7, Corresonding Angles Posulae; 3 7 m 7, Verical Angles Congruence Theorem; m 7, Corresonding Angles Posulae Lesson 3. Geomery Noeaking Guide Coyrigh Hol McDougal. All righs reserved.
3 Your Noes 3. ALTERNATE INTERIOR ANGLES If wo arallel lines are cu by a ransversal, hen he airs of alernae inerior angles are. 3. ALTERNATE EXTERIOR ANGLES If wo arallel lines are cu by a ransversal, hen he airs of alernae exerior angles are. 3.3 CONSECUTIVE INTERIOR ANGLES If wo arallel lines are cu by a ransversal, hen he airs of consecuive inerior angles are. 3 Examle Find he value of x. Use roeries of arallel lines r s 3 (3x ) Soluion Lines r and s are abou arallel lines. (3x ), so you can use he heorems 3x Add o each side. x Divide each side by. The value of x is. Coyrigh Hol McDougal. All righs reserved. Lesson 3. Geomery Noeaking Guide 7
4 Your Noes 3. ALTERNATE INTERIOR ANGLES If wo arallel lines are cu by a ransversal, hen he airs of alernae inerior angles are congruen. 3. ALTERNATE EXTERIOR ANGLES If wo arallel lines are cu by a ransversal, hen he airs of alernae exerior angles are congruen. 3.3 CONSECUTIVE INTERIOR ANGLES If wo arallel lines are cu by a ransversal, hen he airs of consecuive inerior angles are sulemenary. 3 Examle Find he value of x. Use roeries of arallel lines r s 3 (3x ) Soluion Lines r and s are arallel, so you can use he heorems abou arallel lines. 3 (3x ) Alernae Exerior Angles Theorem 7 3x Add o each side. 39 x Divide each side by 3. The value of x is 39. Coyrigh Hol McDougal. All righs reserved. Lesson 3. Geomery Noeaking Guide 7
5 Your Noes Examle 3 Solve a real-world roblem Runways A axiway is being consruced ha inersecs wo arallel runways a an airor. You know ha m 9. Wha is m? How do you know? Soluion Because he runways are arallel, and are. By he Alernae Inerior Angles Theorem, >. By he definiion of congruen angles, m. Checkoin Comlee he following exercises.. Find he value of x. (3x 7) (x ) 3. In Examle 3, suose 3 is he consecuive inerior angle wih. Wha is m 3? Homework Lesson 3. Geomery Noeaking Guide Coyrigh Hol McDougal. All righs reserved.
6 Your Noes Examle 3 Solve a real-world roblem Runways A axiway is being consruced ha inersecs wo arallel runways a an airor. You know ha m 9. Wha is m? How do you know? Soluion Because he runways are arallel, and are alernae inerior angles. By he Alernae Inerior Angles Theorem, >. By he definiion of congruen angles, m m 9. Checkoin Comlee he following exercises.. Find he value of x. (3x 7) (x ) x. 3. In Examle 3, suose 3 is he consecuive inerior angle wih. Wha is m 3? Homework Lesson 3. Geomery Noeaking Guide Coyrigh Hol McDougal. All righs reserved.
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