3.2 Homework. Which lines or segments are parallel? Justify your answer with a theorem or postulate.

Transcription

1 3.2 Homework Which lines or segments are parallel? Justify your answer with a theorem or postulate. 1.) 2.) 3.) ; K o maj N M m/ll = 180 Using the given information, which lines, if any, can you conclude are parallel? Justify each conclusion with a theorem or postulate. 4.) 2 is supplementary to 3 10/12 5.) 6 is supplementary to 7 6.) 4 is supplementary to 8 7.) m 7 = 70, m 9 =110

2 8.) /12 9.) ) ) ) ) ) ) 5 10

3 Find the value of x for which l m. 16.) 17.) m /{x + 25) 18.) 19.) (5x + 40) \m Determine the value of x for which l m. Then find m 1 and m ) m 1= 80 x, m 2 = 90 2x V ^ \ 21.) m 1= 40 4x, m 2 = 50 8x

4 22.) Complete the proof of the following Theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Given: r t, s t Prove: r s Statements Reasons 1. r t 1. Given 2. 1 is a right angle. a. 3. s t 3. Given 4. 2 is a right angle. b c. 6. r s d. 23.) Complete the proof of the following Theorem: If two lines and a transversal form supplementary same-side interior angles, then the two lines are parallel. Given: 1 and 2 are supplementary. Prove: l m Statements 1. 1 and 2 are supplementary 1. Given Reasons 2. m 1 + m 3 = Angle Addition Postulate 3. 1 and 3 are supplementary a. b. 4. Congruent Supplements Theorem: If two angles are supplements of the same angle, then the two angles are congruent 5. l m c.

5 24.) Complete the following proof: Given: a b, 1 2 Prove: l m Statements 1. a b, Given Reasons a b. c. 5. Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. 25.) Complete the following proof: Given: l m, 1 is supplementary to 3 Prove: a b Statements 1. l m, 1 is supplementary to 3 1. Given a. Reasons 3. m 1+ m 3 =180 b. 4. m 4 + m 3 =180 c is supplementary to 4 d. 6. a b e.

6 Answer Key 1. BE CG ; Converse of the Corresponding Angles Postulate 2. CA HR ; Converse of the Corresponding Angles Postulate 3. JO LM ; if two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel. 4. a b ; if two lines and a transversal form same-side interior angles that are supplementary, then the liens are parallel. 5. a b ; if two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel. 6. none 7. none 8. a b ; Converse of the Corresponding Angles Postulate 9. none 10. a b ; Converse of the Alternate Interior Angles Theorem 11. l m ; Converse of the Corresponding Angles Postulate 12. none 13. a b ; Converse of the Corresponding Angles Postulate 14. none 15. l m ; Converse of the Alternate Interior Angles Theorem ; m 1= m 2 = ; m 1= m 2 = 30

7 22. a. Def. of perpendicular lines b. Def. of perpendicular lines c. All right angles are congruent d. Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel 23. a. Definition of Supplementary Angles b. 2 3 c. Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel 24. a. Alternate Interior Angles Theorem: If a transversal intersects two parallel lines, then alternate interior angles are congruent. b. Transitive Property of Congruence c. l m 25. a. Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent. b. Definition of Supplementary Angles c. Substitution d. Definition of Supplementary Angles e. Converse of the Same-Side Interior Angles Theorem: If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel