Proofs with Parallel Lines

Proofs with Parallel Lines Write the meaning of each vocabulary term. converse Vvv..,,..._,._ Theorems Corresponding Angles Converse If two lines are cut Ьу а transversal so the corresponding angles are congruent, then the lines are parallel. j k Alternate lnterior Angles Converse If two lines are cut Ьу а transversal so the altemate interior angles are congruent, then the lines are parallel. !� �Ц:;:-4-S- 'Гitrt � 1\� j k Alternate Exterior Angles Converse If two lines are cut Ьу а transversal so the alternate exterior angles are congruent, then the lines are parallel. Consecutive lnterior Angles Converse If two lines are cut Ьу а transversal so the consecutive interior angles are supplementary, then the lines are parallel. J •+' -4 � u + �Ь ::.{ �(J � ;"\ ) ll )с_ Transitive Property of Parallel Lines If two lines are parallel to the same line', then they are parallel to each other. j k Extra Practice In Exercises 1 and 2, find the value of х that makes т 11 1. (orrtspoмl� qs ::- n. Explain your reasoning. 2. т ��t5S ln Exercises 3-6, decide whether there is enough information to prove that т 11 lf so, state the theorem you would use. 3. т п п. 4. п т п ' 5. -�'лt�,,�\,\ \1\� йЬQ"'� �ood t° .i6�� -Ь �-у r·� м ,·') �r�Ut { -Ь Vi 6. Nи� ho+ п т Proofs with Perpendicular Lines ln your own words, write the meaning of each vocabulary term. distance from а point to а line is �l wt:t у� � s�-ks-t- d.r3� � loof- � ...L !А-�� Theorems J (� 1 ----- -)'�-а.. +(у,-у� Theorem 3.10 Linear Pair Perpendicular Theorem If two lines intersect to form а linear pair of congruent angles, then the lines are perpendicular. g If Ll � L2, then g .l h avcd. Theorem 3.11 Perpendicular Transversal Theorem In а plane, if а transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. j;r 11 k and � then j h j 1. k k Theorem 3.12 Lines Perpendicular to а Transversal Theorem In а plane, if two lines are perpendicular to the same line, then they are parallel to each other. then т lln m п р Extra Practice ln Exercises 1-4, find the distance from point.:A to вё. 1. 2. ? i....+---«c"+--+--+-r-t--+--+4-.-xi 1 D(-1, -2) 1 �, ' �'\А� _ s � '1 +е')�. . t........__":,--..-\.�••I,-•,..'✓•�--:" V ,--·,,<- (: 'l� + 1''1 1.. '.-.- о (-z], •• . 'r' ( �)� 1�{ с,!. ;·1\ 4 l•'l/:С .... ti+t)l.. г�----=-' ) - t ( 2..·1 � (.- Z-.Г f +- �( _, � - 3 · .--.-----,-..-.-., г--т--,:-. ..-----.------, ji,,ь � ,1.. l�Ю 4. -4 2 -2 -4 � у А (1, 3) / 1- С/ � (З, 2) l ' IJI 1Г" / 4х ) В(1, -2) D(O, -4) f 1 ···�•-.-:'"'i_,..., ... 1;�•-:-.• � _t -. �"'•' ,. .... .... r 1,(-�- -; ,�)1. +-(-) -ЕО, (.. - ._ � ...., .• ,.-.,.; -_..-. - . � ,. i( Г(- Lf),._ + (. -� t ,�:., .. r- : J l�+Ч � .г;-Q_" � �;- :. 1.(� ,-- • s ._ ' ;, 1 - ?> '\ l. +- (_ � .... 2- �- v ч + 1 ,, IJ (-t.i\ i + (-2-'\1. V . 2 ....__.:.., : гJ \ '\ (,·t 1 ( d t,(Clil J")y: 4-' /·' ln Exercises 5-8, determine which lines, if any, must Ье parallel. Explain your reasoning. 5. р q 6. р .J_ � s 1\) с>.\ � е r о� 1 "'r h Gi ""it :) р l! q, и�г� ri.t. /,•''ferpt'v'-oli ci,i ·�:; L; ,..� т 7. п 8. т - п j s k t t&i-r �i-\ tt. �,�oro 42,.-:.,q () f; j_ (\ �$1� 1 L.,: i i'\ е. а. 11'· � 1.., \�. Pef'f>P"'t;lic ,,.� (.) Ре, ff61d. ct i,. 'f\e. L ,,..� �\.е. �Ct\ 1е 1J(( tl.L Ci V\" J Ре,,., �"' с1; с &1 k" L. i\.-L g� le_