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Day 4 Section 2.5.notebook October 06, 2014 Day 4 2.5 Proving Angles Congruent Objectives: To identify angle pairs To prove and apply theorems about angles G.1.A, M.2.B Performance Standard 1.8, 3.5, 4.1 DOK1, 2 Knowledge MA 2, MA 1 Day 4 Section 2.5.notebook October 06, 2014 Vertical Angles: "across from each other" 2 3 1 4 Vertical Angles are congruent. How should we code them? 2 Day 4 Section 2.5.notebook October 06, 2014 Name the vertical angles below: D A C B E 3 Day 4 Section 2.5.notebook October 06, 2014 Adjacent angles: 1) Share an entire side 2) Share a vertex 3) Do NOT overlap! D C E F O B A Identify adjacent angles in the diagram above 4 Day 4 Section 2.5.notebook October 06, 2014 Ex 1) Are these angles adjacent? Why or why not?? B A <AOB and <BOC C O S R W <RXS and <SWT T X 5 Day 4 Section 2.5.notebook P N October 06, 2014 <NPM and <QNP M Q V <ESV and <VSD E S D 6 Day 4 Section 2.5.notebook October 06, 2014 Complementary Angles: add up to 90 degrees. 30 2 60 1 Supplementary Angles: add up to 180 degrees. 120 60 Linear Pairs are SUPPLEMENTARY! 7 Day 4 Section 2.5.notebook October 06, 2014 Z Examples: <XAY = ________ X P 45o A <ZAP and ______________ are supplementary Y <XAY and _______________ are complementary M <ZAX and ______________________ are vertical. m<PAZ = _____________________ 8 Day 4 Section 2.5.notebook October 06, 2014 Assignment portions taken from pg 100 of Geometry textbook Name: ________________________________________________________ Date: ____________________________ Block: _________ Section 2.5 Proving Angles Congruent and Angle Relationships For #15, name an angle or angles in the diagram described by each of the following: 1. supplementary to <AOD A E 3. supplementary to <EOA 60o 4. complementary to <EOD D 5. two pairs of vertical angles 6. What is the measure of <DOC? B 2. adjacent and congruent to <AOE O C 7. What is the measure of <COB? 8. What is the measure of <EOB? Each conditional statement below is true. b) Is the converse true or false? a) Write the converse. c) If the converse is false, provide a counterexample. 9. If y + 7 = 32, then y = 25. a) b) c) 10. If you live in Australia, then you live south of the equator. a) b) c) 9 Day 4 Section 2.5.notebook October 06, 2014 11. If n > 0, then n2 > 0. a) b) c) 2 12. Solve: x 4 = 8 7 13. Write the equation of the line shown on the graph in slopeintercept form. 14. Rewrite the following sentence as a conditional statement: All of the trees in Redwood National Forest are beautiful. 10