Parallel and Perpendicular Lines
INTEGRATED I PARALLEL LINESSUCCESS CRITERIA:Determine if lines are intersecting, parallel, or skew. Use two-column proofs to justify statements regarding parallel lines. Determine the value of angles formed by a transversal and parallel lines323913531750063503810003406140-317500224790-254000224790190500INSTRUCTOR: Craig ShermanHidden Lake High SchoolWestminster Public SchoolsEMPOWER Recorded TARGETSCALE THEME MA.09.G.01.04Using Coordinates to find Distance FormulaPROFICIENCY SCALE:SCOREREQUIREMENTS4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class. Score 4.0 does not equate to more work but rather a higher level of performance.3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success.o Determine the appropriate solution in a Real World example.3.0The learner exhibits no major errors or omissions regarding any of the information and processes (simple or complex) that were explicitly taught.o?Determine if lines are intersecting, parallel, or skew, ANDo Use two-column proofs to justify statements regarding parallel lines ANDo Determine the value of angles formed by a transversal and parallel lines.2.0 Can do one or more of the following skills / concepts: There are no major errors or omissions regarding the simpler details and processes as the learner…o?Identify if lines are intersecting, parallel, or skew, ORo Identify the pairs of angle formed by parallel lines cut by a transversal, ORo Determine the value of a linear pair of angles, OR o Determine the value of a linear pair of angles, OR o Determine the value of alternate interior angle, OR o Determine the value of alternate exterior angles, OR o Determine the value of vertical angles, OR o Determine the value of corresponding angles, OR o?Prove statements about parallel lines using two-column proofs1.0 Know and use the vocabulary Identify the Basic ElementsWith help, a partial understanding of some of the simpler details and processLINES: Intersecting, Parallel & Skew WORD or CONCEPT DEFINITION or NOTESEXAMPLE or GRAPHIC REPRESENTATIONintersecting????parallel????skew????coplanar????INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2: SOPHIA Class Work – Use image 1 4100508171101Name all segments parallel to GH:Name all segments skew to GH QUOTE : Name all segments intersecting with GH QUOTE : Are segments GH QUOTE and BA coplanar? Explain your answer. Are segments GH and BF coplanar? Explain your answer. Is each statement true always, sometimes, or never?6. Two intersecting lines are skew.7. Two parallel lines are coplanar.8. Two lines in the same plane are parallel.9. Two lines that do not intersect are parallel.4953000141605Image 100Image 110. Two skew lines are coplanarHomework - Use Image 1 Name all segments parallel to FE QUOTE :Name all segments skew to FE: Name all segments intersecting with FE:Are segments FE and CDcoplanar? Explain your answer.Are segments FE and HD QUOTE coplanar? Explain your answer. State whether the following statements are always, sometimes, or never true:Two coplanar lines are skew.Two intersecting lines are in the same plane.Two lines in the same plane are parallel.Lines & TransversalsWORD or CONCEPT DEFINITION or NOTESEXAMPLE or GRAPHIC REPRESENTATIONparallel lines????transversal????same side interior angles????same side exterior angles????corresponding angles????alternate interior angles????alternate exterior angles????INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2: SOPHIA Class Work right10795Classify each pair of angles as alternate interior, alternate exterior, same-side interior, same-side exterior, corresponding angles, or none of these.19. QUOTE ∠11 and ∠16 are20. QUOTE ∠12 and ∠2 are21. ∠14 and ∠8 are QUOTE 22. QUOTE ∠6 and ∠16 are23. QUOTE ∠7 and ∠14 are24. QUOTE ∠3 and ∠16 areHomeworkClassify each pair of angles as alternate interior, alternate exterior, same-side interior, same-side exterior, corresponding angles, or none of these.1981200-693420∠7 and ∠12∠3 and ∠6∠6 and ∠11∠7 and ∠11∠4 and ∠10∠14 and ∠16∠2 and ∠3∠2 and ∠10Parallel Lines & ProofsWORD or CONCEPT DEFINITION or NOTESEXAMPLE or GRAPHIC REPRESENTATIONproof????statement????reason????substitution????transitive property????reflexive property????symmetric property????INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2: SOPHIA ClassworkMatch each expression/equation with the property used to make the conclusion. AB = AB If m∠A = m∠B and m∠B = m∠C, then m∠A = m∠C. If x + y = 9 and y = 5, then x + 5 = 9. If DE = FG, then FG = DE.Substitution Property of EqualityTransitive Property of EqualityReflexive Property of EqualitySymmetric Property of EqualityPARCC type question:362458033909000 Alternate Exterior Angles Proof: Complete the proof by filling in the missing reasons with the “reasons bank” below.Given: line m || line kProve: ∠2 ? ∠8StatementsReasons1. line m || line k1. 2. ∠2 ? ∠62. 3. ∠6 ? ∠83. 4. ∠2 ? ∠84. -16256055880Reasons BankTransitive Property of CongruenceIf 2 parallel lines are cut by a transversal, then the corresponding angles are congruent. Vertical Angles are congruent.Given00Reasons BankTransitive Property of CongruenceIf 2 parallel lines are cut by a transversal, then the corresponding angles are congruent. Vertical Angles are congruent.GivenHomeworkFor #39-42 match the description on the left to the name of the property on the right. ∠A ? ∠B and ∠B ? ∠C, then ∠A ? ∠C.a) Substitution Property of Equality If bc = 77 and b = 11, then 11c = 77.b) Transitive Property of Congruence If ∠P ? ∠M, then ∠M ? ∠P. c) Reflexive Property of Equality QR = QRd) Symmetric Property of CongruencePARCC type question: Alternate Interior Angles Proof: Complete the proof by filling in the missing reasons with the “reasons bank” below.383095513906500Given: line m || line kProve: ∠3 ? ∠5StatementsReasons1. line m || line k1. 2. ∠3 ? ∠72. 3. ∠7 ? ∠53. 4. ∠3 ? ∠54. -37166551248410Reasons BankVertical Angles are congruent.GivenTransitive Property of CongruenceIf 2 parallel lines are cut by a transversal, then the corresponding angles are congruent. 00Reasons BankVertical Angles are congruent.GivenTransitive Property of CongruenceIf 2 parallel lines are cut by a transversal, then the corresponding angles are congruent. 2554310-158071Properties of Parallel LinesClasswork Use the given diagram to answer problems #33-41.If m∠9 = 54°, then find the measure the following angles:m∠1=m∠2=m∠4=m∠5= QUOTE m∠15=If m∠2 = (12x-54)° and m∠10 = (7x+26)°, then find the measure the following angles: -16692521480950.m∠6=51. m∠11=right17331052. m∠9= 53. m∠16=Find the values of the unknown variables in each figure. 54.56.right7727237186155503State which segments (if any) are parallel.56.57.Solve for the unknowns274320762058. 2486463-701800Homework If m QUOTE ∠9 = 62°, then find the measure the following angles:59. m∠1=60.m∠2=61.m∠4=62.m∠5=63m∠15=If m QUOTE ∠2 = (14x-24)° and m QUOTE ∠10 = (6x+72)°, then find the measure the following angles: 64.m∠6=65m∠11=66m∠9=67.m∠16=Find the values of the unknown variables in each figure. (#78-82)30827281276368. 69.2151041389800357116913710State which segments (if any) are parallel.70 71. . 1606693201205 72. PARALLEL LINE SUMMARYANGLES?????????????ADJACENTSAME SIDEALTERNATEVERTICALLINEAR PAIR???82559080500??????-17145-6350000?INTERIOREXTERIORCORRESPONDING?1-int1-ext??????INTERIOREXTERIORSupplementary9715508890?00?CONGRUENT ( )?Def of suppl??803275-52705?00?Def of ????????+?=180??=??Parallel Lines UNIT ReviewMultiple ChoiceName the segment parallel to GH and skew to EA. QUOTE a. FBb. DA 356602616617c. JId. HDName the segment parallel to BCand skew to EI.a. FBb. DA c. JId. HDDetermine if the statement is always, sometimes, or never true: Two skew lines are coplanar.a. Alwaysb. QUOTE Sometimes c. Never Determine if the statement is always, sometimes, or never true: Two intersecting lines are coplanara. Alwaysb. QUOTE Sometimes c. Never Determine if the statement is always, sometimes, or never true: Two lines that do not intersect are skew.a. Always2895600100965b. QUOTE Sometimes c. Never Determine the relationship between ∠1 & ∠10.a. Alternate Interiorb. Same-side Interiorc. Corresponding Anglesd. None of theseDetermine the relationship between ∠5 & ∠15.a. Alternate Exteriorb. QUOTE Alternate Interior c. Same-side Interiord. None of theseGiven in the diagram to the right, m∠2=3x-10 QUOTE and m∠15=2x+30 QUOTE , what is m∠12? QUOTE a. 32o320040034290b. 40oc. 86od. 110oGiven in the diagram to the right, m∠5= (7x+2)°and m∠11=(5x+14)°, what is m∠14?a. 6°b. 44°266700045720c. 46°d. 136°In 10-11, use the diagram at the right. Given ∠2 ? ∠6, what justifies k || m.a. Converse Alternate Interior Angles Theoremb. Converse Alternate Exterior Angles Theoremc. Converse Corresponding Angles Theoremd. there is not enough info to state parallelGiven n || p , what justifies ∠1 ? ∠12a. Alternate Interior Angles Theoremb. Alternate Exterior Angles Theoremc. Corresponding Angles Theoremd. there is not enough info to make this statementExtended Constructed Response373380011430001. Complete the proof by filling in the missing reasons with the “reasons bank” to the right. Some reasons may be used more that once.Given: QUOTE ∠1 ? ∠3; MN || PQProve: ∠2?∠3Statements155892558420Reasons Banka) Transitive Property of Congruenceb) If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent. c) Given00Reasons Banka) Transitive Property of Congruenceb) If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent. c) GivenReasons1. ∠1 ? ∠31. 2. MN || PQ2. 3. ∠1 ? ∠23. 4. ∠2?∠34. 44646763026532. Complete the proof by filling in the missing reasons with the “reasons bank” to the right. Some reasons may be used more that once.Given: n || p, k || mProve: QUOTE ∠2 & ∠13 are supplementaryStatementsReasons1. n || p, k || m1. 2. ∠2 ? ∠12 QUOTE 2. 3. ∠12 ? ∠14 QUOTE 3. 4. ∠2 ? ∠144. 5. m∠2 = m∠14 5. 6. m∠13 & m∠14 are supplementary QUOTE 6. 7. m∠13 + m∠14 = 180° QUOTE 7. 8. m∠13 + m∠2 = 180° QUOTE 8. 9. ∠2 &∠13 are supplementary9. 39793348683Reasons Banka) Transitive Property of Congruenceb) Definition of supplementary anglesc) If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent. d) Definition of Congruent Anglese) Givenf) If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent.g) Angles that form a linear pair are supplementaryh) Substitution Property of Equality00Reasons Banka) Transitive Property of Congruenceb) Definition of supplementary anglesc) If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent. d) Definition of Congruent Anglese) Givenf) If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent.g) Angles that form a linear pair are supplementaryh) Substitution Property of Equality ................
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