Chapter Start Thinking. 3.1 Warm Up. 1. Sample answer: 3. CG. 5. Sample answer: FE and FG. 6. Sample answer: D. 3.

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1 7. ( x + )( x 7) 8. ( x )( x + ) 9. ( x 7)( x + ) 0. ( x 5)( x ). ( x )( x ). ( x + )( x 9) Chapter. Start Thinking B. ( x + )( x ). ( x + )( x ) 5. ( x + 5)( x 5) 6. ( x )( x + ) A C 7. ( x 5)( x 7) 8. ( 5x + )( x + ) 9. x = 8 and x = 0. x = 6 and x =. x = and x =. x = 9 and x = 8. x = 5 and x =. x = 0 and x = 7 5. x = and x = 6. x = 5 and x = 7. x = and x = 8. and = and = x = and x = 5. a. 7 words per min b words c. 05 words d. 7.5 words right triangle; no; no; Because points B and C connect perpendicular lines, ou cannot plot either point to make a perpendicular segment or a parallel segment.. Warm Up. Sample answer: BC. GE. CG. AB, BC, BD 5. Sample answer: FE and FG 6. Sample answer: D. Cumulative Review Warm Up. K (, ). J ( 7, 8). K (, ). ractice A. AB and CD. AC and CD. no; AB CD and b the arallel ostulate (ost..), there is exactl one line parallel to AB through point C.. no; The are intersecting lines. 5. and 8, and 5 6. and 7, and 6 7. and 5, and 6, and 7, and 8 8. and 5, and 8 9. no; B definition, skew lines are not coplaner. 0. pairs; pairs; ( n ) pairs. a. AB and CD, AC and BD b. AC and CD, BD and CD c. and 5, and 8 A Geometr Copright Big Ideas Learning, LLC

2 d. and 5, and 6, and 7, and 8 e. and 8, and 5 f. and 7, and 6. ractice B. lines c and d. lines e and f. Sample answer: lines c and e a. b c. Line a appears to be parallel to line c; If two lines are parallel to the same line, then the are parallel to each other. n. planes A and B 5. no; lines f and g appear to be coplanar and although the do not intersect, there is not enough information to determine that the lines are parallel. 6. no; lines e and g appear to be coplanar and intersect at a 90 angle, but there is not enough information to determine that the lines are perpendicular. 7. alternate interior 8. corresponding 9. alternate exterior 0. corresponding. consecutive exterior. no; The lines do not intersect, however the could be coplanar to a third plane.. m Line seems to be parallel to line n; If two lines are perpendicular to the same line, then the are parallel to each other. n m. a. true; The road and the sidewalk appear to lie in the same plane and the do not intersect. b. false; The road and the crosswalk appear to intersect. c. true; A properl installed stop sign intersects the ground at a 90 angle. 5. B A. Enrichment and Extension. es; The two lines of intersection are coplanar because the are both in the third plane. The two lines do not intersect because the are in parallel planes. Because the are coplanar and do not intersect, the are parallel. 6. a. 5,, 7 b. 5, 9, 7 c. 8,, 7 d. 7, 9, 8 e., 0, f., 0, 6 g.,, 5 h. 5. uzzle Time A YARDSTICK Copright Big Ideas Learning, LLC Geometr A

3 . Start Thinking one angle measure; With the measurement of one of the, ou can use the properties of corresponding, alternative interior, alternate exterior, and consecutive interior to find the other seven measurements.. Warm Up Cumulative Review Warm Up A t A C 5 C m D D B B R R R. ractice A. m = 87, m = 9 ; m = 87 b the Alternate Interior Angles (Thm..). m = 9 b the Consecutive Interior Angles (Thm..).. m = 78, m = 78 ; m = 78 b the Corresponding Angles (Thm..). m = 78 b the Alternate Exterior Angles (Thm..).. 8; 7 ( 6x ) = 8 = 6x 8 = x. 0; m + = 80 ( x + 9) + = 80 x = 80 x + 60 = 80 x = 0 x = 0 5. m =, m = 68, m = ; Because the angle is a vertical angle to, b the Vertical Angles Congruence (Thm..6) the are congruent. Because and are consecutive interior, the are supplementar b the Consecutive Interior Angles (Thm..). Because the given angle and are alternate exterior, the are congruent b the Alternate Exterior Angles (Thm..). 6. m = 5, m = 5, m = 5; Because the given 5 angle is a corresponding angle with, and is a corresponding angle with, the are all congruent b the Corresponding Angles (Thm..). Because the 5 angle is a consecutive interior angle with, the are supplementar b the Consecutive Angles (Thm..).. R S x A Geometr Copright Big Ideas Learning, LLC

4 7. 8. t p. p q. Given. m + m = 80. Linear air ostulate (ost..8). m + m = 80. Consecutive Interior Angles (Thm..).. Congruent Supplements (Thm..).. Given q.. Vertical Angles Congruence (Thm..6).. Transitive ropert of Angle Congruence (Thm..) m = 90 ; Because is congruent and supplementar to, the measure of each angle is = x + = x = x 6 = x. 6; ( x ) ( x 8) = 80. 5; ( x ) ( x ) x x 5 = 80 x 7 = 80 x = 5 5. m = 0, m = 0, m = 78 ; Because the given 0 angle is an alternate interior angle with, the are congruent b the Alternate Interior Angles Congruence (Thm..). Because the given 0 angle and are alternate exterior, the are congruent b the Alternate Exterior Angles (Thm..). Because and are a linear pair, the are supplementar b the Linear air ostulate (ost..8). 6. m = 68, m = 68, m = ; Because the given 68 angle and are corresponding, the are congruent b the Corresponding Angles (Thm..). Because and are alternate exterior, the are congruent b the Alternate Exterior Angles (Thm..). Because angle and are consecutive, the are supplementar b the Consecutive Interior Angles (Thm..). 7. m = 0, m = 70 ; Because ( x 5) ( x 0 ), ( x + 5) = 0 and ( ) + = the value of x is 5. So, x 0 = 0. B the Corresponding Angles (Thm..), m = 0. B the Linear air ostulate (ost.8), m = 70.. ractice B. m =, m = ; m = b the Corresponding Angles (Thm..). m = b the Vertical Angles Congruence (Thm..6).. m =, m = ; m = b the Alternate Exterior Angles (Thm..). m = b the Vertical Angles Congruence (Thm..6). Copright Big Ideas Learning, LLC Geometr A5

5 8., 5, 6, 7, 9, and 0; Because and are supplementar to b the Consecutive Interior Angles (Thm..), b the Congruent Supplements (Thm..). 5and 7b the Alternate Interior Angles (Thm..). 6b the Vertical Angles Congruence (Thm..6). Because 9b the Vertical Angles Congruence (Thm..6), 9b the Transitive ropert of Angle Congruence (Thm..). Because 5 0b the Vertical Angles Congruence (Thm..6), 0b the Transitive ropert of Angle Congruence (Thm..).. Enrichment and Extension. x = 65, = 60. x =, =. A D. m = 5, m = 5, m =, m = 69, m 5 =, m 6 = 69, m 7 = 5, m 8 = 5, m 9 = 69, m 0 =, m = 69, m =, m = 76, m = 0, m 5 = 76, m 6 = 0, m 7 = 0, m 8 = 76, m 9 = 0, m 0 = m = 00, m = 80, m = 80, m = 00, m 5 = 00, m 6 = 56, m 7 =, m 8 =, m 9 = 56, m 0 = 00, m = 56, m =, m =, m = 56, m 5 =, m 6 = 56, m 7 =, m 8 = 56, m 9 = 00, m 0 = 80, m = 00, m = 80, m = 56, m =, m 5 =, m 6 = 56, m 7 = 00, m 8 = 56, m 9 =, m 0 =, m = 56, m = 00 B C. uzzle Time GEOMETRY. Start Thinking. AB DC, AD BC. Given. A and B are supplementar.. B and C are supplementar.. Consecutive Interior Angles (Thm..). Consecutive Interior Angles (Thm..). m A + m B = 80. Definition of supplementar 5. m B + m C = Definition of supplementar 6. m A + m B = m B + m C 6. Substitution 7. m A = m C 7. Subtraction ropert of Equalit 8. A C 8. Definition of congruent 0 ; 60 and 0, respectivel; The are the same as the shopping mall sidewalks because the are parallel to them.. Warm Up. x = 9, =. x = 0, =. Cumulative Review Warm Up. m = m. GH + HJ. GH. ractice A 60 walkwas Shopping Mall streets 60. x = ; Lines s and t are parallel when the marked alternate exterior are congruent. ( x 8) = ( x + 0) x = x + 0 x = A6 Geometr Copright Big Ideas Learning, LLC

6 . x = 8; Lines s and t are parallel when the marked consecutive interior are supplementar. ( x ) + 0 = 80 x + 08 = 80 x = 7 x = 8. es; Corresponding Angles Converse (Thm..5). no 5. This diagram shows that the vertical are congruent, and we do not have enough information to prove that m n. 6.. and are supplementar.. and are supplementar.. Given. Linear air ostulate (ost.8).. Congruent Supplements (Thm..). p q. Corresponding Angles Converse (Thm..5) 7. no; The labeled must be congruent to prove the wings are parallel.. ractice B. x = ; Lines s and t are parallel when the marked alternate exterior are congruent. ( x + 6) = ( 7x 0) 6 = x = x. x = 6; Lines s and t are parallel when the marked consecutive interior are supplementar. ( x + 5) + ( x + 0) = 80 x x + 0 = 80 5x + 50 = 80 5x = 0 x = 6. es; Alternate Exterior Angles Converse (Thm..7). es; Consecutive Interior Angles Converse (Thm..8) 5. a. es; Lines a and b are parallel b the Alternate Interior Angles Converse (Thm..6). Lines b and c are parallel b the Alternate Exterior Angles Converse (Thm..7). Line c and d are parallel b the Corresponding Angles Converse (Thm..5). Lines b and c are parallel b the Alternate Exterior Angles Converse (Thm..7). B the Transitive ropert of arallel Lines (Thm..9), all the lines of latitude are parallel. b. no; There is not enough information to prove that the lines of longitude are parallel. 6. a. x = 7, =, z = 9; Lines p and q are parallel when the marked alternate exterior are congruent. ( x + ) = ( x 0) x = x 0 7 = x Lines q and r are parallel when the marked corresponding are congruent. ( x 0) = ( 6) 7 ( ) 0= 6 78 = 6 = The 6 and 6( z + 8) form a linear pair, so the are supplementar ( z + 8) = 80 6 ( ) + 6( z + 8) = z + 8 = 80 6z = 5 z = 9 x = 78 and 6 = 78, b. es; Because ( ) lines p and q are parallel b the Alternate Exterior Converse (Thm..7). Copright Big Ideas Learning, LLC Geometr A7

7 7.. Enrichment and Extension Given. c d. Alternate Exterior Angles Converse (Thm..7).. Given. a b. Alternate Interior Angles Converse (Thm..6) Corresponding Angles (Thm..) Transitive ropert of Angle Congruence (Thm..).. AC is parallel to FG. BD is the bisector of CBE. DE is the bisector of BEG.. Given. CBE BEF. Alternate Interior Angles (Thm..). m CBE = m BEF. roperties of Angle Congruence (Thm..). ABE BEG. Alternate Interior Angles (Thm..) 5. m ABE = m BEG 5. roperties of Angle Congruence (Thm..) 6. CBE + ABE = Definition of linear pair CBE + BEG = Substitution CBE = DBE 8. Definition of angle bisector BEG = BED 9. Definition of angle bisector CBE + BEG 0. Multiplication ropert of = ( 80 ) Equalit. CBE + BEG = 90. DBE + BED = 90. m DBE + m BED + m EDB = 80. Simplif. Substitution. ropert of tri. 80 = 90 + EDB. Substitution EDB = 5. Subtraction ropert of Equalit A8 Geometr Copright Big Ideas Learning, LLC

8 . a. one line b. an infinite number of lines c. one plane. a. 7 b. 7 c. 7 d. e CA ED m FED = 5. ABE and DEB are supplementar.. uzzle Time m ABE + m DEB = 80. m ABE + 5 = 80. Given. Consecutive Interior Angles (Thm..). Definition of supplementar. Substitution ropert of Equalit 5. m ABE = 5 5. Subtraction ropert of Equalit 6. m FBC = 5 6. Vertical Angles Congruence (Thm..6) 7. m GCA = 5 7. Given = Addition 9. m FBC + m GCA = FBC and GCA are supplementar. 9. Substitution ropert of Equalit 0. Definition of supplementar.. EF CG. Consecutive Interior Angles Converse (Thm..8) BECAUSE HE WANTED TO SEE TIME FLY. Start Thinking Sample answer: framing square and chalk line; A framing square ensures cuts made with saws are precise. The chalk line helps builders keep a horizontal surface when needed.. Warm Up. 5 cm. cm cm. 6 cm 5. 7 cm. Cumulative Review Warm Up. Given AB CD, prove CD AB. Given A, prove A A. ractice A. about 5.7 units.. AB CD. Given. AB = CD. Definition of congruent segments. CD = AB. Smmetric ropert of Equalit. CD AB. Definition of congruent segments. A. Given. m A = m A. Reflexive ropert of Angle Measures. A A. Definition of congruent m. none; The onl thing that can be concluded from the diagram is that n and m p. In order to sa that the lines are parallel, ou need to know something about the intersections of and p or m and n. Copright Big Ideas Learning, LLC Geometr A9

9 . b c; Because a band a c, lines b and c are parallel b the Lines erpendicular to a Transversal (Thm..) Given. e h. Linear air erpendicular (Thm..0). e f. Lines erpendicular to a Transversal (Thm..). e g. Transitive ropert of arallel Lines (Thm..9) 6. no; There is onl one perpendicular bisector that can be drawn, but there is an infinite number of perpendicular lines. 7. w x, w z, x z; Because w b and x b, w x b the Lines erpendicular to a Transversal (Thm.). Because w b and z b, w z b the Lines erpendicular to a Transversal (Thm.). Because w x and w z, x z b the Transitive ropert of arallel Lines (Thm..9).. ractice B. 5 units. g h ; Because e g and e h, lines g and h are parallel b the Lines erpendicular to a Transversal (Thm..).. n, m n, m; Because j and j n, lines and n are parallel b the Lines erpendicular to a Transversal (Thm..). Because k m and k n, lines m and n are also parallel b the Lines erpendicular to a Transversal (Thm..). Because n and m n, lines and m are parallel b the Transitive ropert of arallel Lines (Thm..9).. es; Because e f, a eand c e, lines a and c are perpendicular to line f b the erpendicular Transversal (Thm..). Because a f, b f, c f, and d f, b the Lines erpendicular to a Transversal (Thm..) and the Transitive ropert of arallel Lines (Thm..9), lines a, b, c, and d are all parallel to each other Given. a c. Linear air erpendicular (Thm..0). c d. Given. a d. erpendicular Transversal (Thm..9) 5. b d 5. Given 6. a b 6. Lines erpendicular to a Transversal (Thm..) 6. m = 90, m = 5, m = 90, m = 5, m 5 = 5 ; m = 90, because it is vertical with a right angle, so it has the same angle measure. m = = 5, because it is complementar to the 75 angle. m = 90, because it is marked as a right angle. m = 75 0 = 5, because together with the 0 angle, the are vertical with the 75 angle, so the angle measures are equal. m 5 = 5, because it is vertical with, so the have the same measure. 7. no; You do not know anthing about the relationship between lines x and or x and z. A0 Geometr Copright Big Ideas Learning, LLC

10 . Enrichment and Extension.. AC BC ; is complementar to. is complementar to. m + m = 90. m + m = m + m = m + m. Given. Definition of perpendicular lines. Definition of complementar. Definition of complementar 5. Substitution 6. m = m 6. Substitution ropert of Equalit 7. m = m 7. Smmetric ropert of Equalit Definition of congruent.. AB bisects DAC ; CB bisects ECA m 5 m = = 5. Given. m = m. Definition of angle bisector. m = 5. Substitution. m + m = m DAC = m DAC. Angle addition 5. Substitution = m DAC 6. Simplif 7. DAC is a right angle 8. DA AC 7. Definition of a right angle 8. Definition of perpendicular lines 9. m = m 9. Definition of angle bisector 0. m = 5 0. Definition of congruent. m + m. Angle addition = m ECA = m ECA. Substitution. 90 = m ECA. Simplif. ECA is a right angle. 5. EC AC 6. AD is parallel to CE.. Definition of a right angle 5. Definition of perpendicular lines 6. Lines erpendicular to a Transversal (Thm..) Copright Big Ideas Learning, LLC Geometr A

11 ... j,. Given. m + m = 90. Definition of complementar. m = m. Definition of congruent. m + m = BED is a right angle. m n. Given. and 6 are complementar.. and are complementar.. Definition of complementar. Given. 6. Congruent Complements (Thm..5) Vertical Angles Congruence (Thm..6) Transitive ropert of Congruence (Thm.). Substitution 5. Definition of a right angle 6. k m 6. Definition of perpendicular lines.5 Start Thinking = x + = x + 5 x = x The lines = x and = x + do not intersect; The line = x + 5 intersects the line = x at the point (, ) and the line = 7 x + at the point, ; The are right..5 Warm Up. = 6x 6 6 x. = x x 5. d = 7 6. d = d = 8.. uzzle Time THE ADDER d =. x = x A Geometr Copright Big Ideas Learning, LLC

12 . = x + x 5. = x = 6x = x = x no; For a line with a slope between 0 and, the slope of a line perpendicular to it would be negative. x. ( 5, ) = x.5 ractice B. Q = (.5, ). Q = ( 0, ) 6. = x + x = =, lines 6 and are neither parallel nor perpendicular.. neither; Because m m ( ). = 6x 0 5. = x + 6. about.5 7. about..5 Cumulative Review Warm Up. Multiplication ropert of Equalit. Subtraction ropert of Equalit. Reflexive ropert of Equalit for Real Numbers. Reflexive ropert of Equalit for Angle Measures 5. Transitive ropert of Equalit for Angle Measures 6. Smmetric ropert of Segment Lengths.5 ractice A. (.5, ). ( 0,.). perpendicular; Because 9 m m = =, lines and are 9 perpendicular b the Slopes of erpendicular Lines (Thm..). 5. neither; Because m m = =, lines 5 and are neither parallel nor perpendicular. 8. Sample answer: b = 5, c = 9. a. The slope is m,where m < 0. b. The slope is m,wherem. c. The lines are perpendicular; The are perpendicular b the erpendicular Transversal (Thm..). 0. es; Sample answer: The lines = xand = x have the same -intercept and the slopes are negative reciprocals.. 5,.5 Enrichment and Extension. = x. a = 8, b = 0. a..6 b..7 c. =.6x d. = 0.76x. Copright Big Ideas Learning, LLC Geometr A

13 . a ; parallel: = ax ; perpendicular: = b x b b a 5. k =, = x k can have an value, = x 5 7. a. ae db b. a d, b 0, e 0 b = e 8. a. Sample answer: (, ), (, ), ( 0, ) b. Sample answer: x =, x =, x = 0, =, =,,,, 0, c. ( ) ( ).5 uzzle Time DRO THE S Cumulative Review a. A.M. b. 6.5 in. c..m. 5. a. about $.9 b. about $9.90 c. about $ x = 6 7. x = 8 8. x = 6 9. x = 5 0. x =. x = 8. x = 9. x = 9. x = 5. x = 6. x = 7. x = 8. x = 9. x = 50. x = 6 5. x = 5 5. m =, b = 5. m =, b = 5 5. m =, b = 7 m = 6, b = 56. m =, b = m =, b = 58. m =, b = 59. m =, b = m =, b = 8 6. m =, b = 5 6. m 6. m =, b = 6. 0x 65. a. 8 5 = b =.5 5 =, b = 8 7 c. Compan A is minutes faster. Compan B is.5 minutes faster (, 5.5) 79. ( 8, ) 80. (.5, ) 8. (.5, ) 8. (.5, 9.5) 8. (, 0.5) 8. ( 5.5, ) 85. ( 0.5, 7) 86. ( 5.5,.5) 87. ( 0.5,.5) 88. (.5, 0.5) 89. ( 0.5, 0.5) 90. a. each individual visit b. each individual visit c. 5 or more visits A Geometr Copright Big Ideas Learning, LLC

14 9. a. $7.80 b. $9.70 c. 7 lb 9. = x 9. = x 7 x = = x +.. x x 96. = x = 8x = x = x 0. x 5 5 = + = x + 0. = 9 x 0 0. = x + 0. = x = = x x = x = x = 8 0. x = 9. x = 5. x = (, 0) (, 5) (6, 0) (, ). Cumulative Review Warm Up. 6 x t 6 x Chapter. Start Thinking B B Translate the original triangle units down; Each ordered pair for Δ A BC contains -coordinates that are two less than those of ΔABC; When identifing a translation, ou can compare the x- and -values to determine what happens if the figure is plotted.. Warm Up.. A A C C x p q Given p q rove. p q. Given.. Corresponding Angles (Thm..).. Vertical Angles Congruence (Thm..6).. Transitive ropert of Angle Congruence (Thm..) x x (, ) (0, ) Copright Big Ideas Learning, LLC Geometr A5