Lesson 5.1 Polygon Sum Conjecture

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1 Lesson 5.1 olgon Sum onjeture me eriod te In erises 1 nd 2, find eh lettered ngle mesure. 1.,,, 2.,,, d, e d, e, f d e e d 97 f ne eterior ngle of regulr polgon mesures 10. Wht is the mesure of eh interior ngle? How mn sides does the polgon hve? 4. The sum of the mesures of the interior ngles of regulr polgon is How mn sides does the polgon hve? 5. is squre. is n equilterl 6. is regulr pentgon. FG tringle. is squre. G F 7. Use protrtor to drw pentgon with m 85, m 125, m 110, nd m 70. Wht is m? esure it, nd hek our work lulting. 32 HT 5 isovering Geometr rtie Your Skills 2008 Ke urriulum ress

2 Lesson 5.2 terior ngles of olgon me eriod te 1. How mn sides does regulr polgon hve if eh eterior ngle mesures 30? 2. How mn sides does polgon hve if the sum of the mesures of the interior ngles is 3960? 3. If the sum of the mesures of the interior ngles of polgon equls the sum of the mesures of its eterior ngles, how mn sides does it hve? 4. If the sum of the mesures of the interior ngles of polgon is twie the sum of its eterior ngles, how mn sides does it hve? In erises 5 7, find eh lettered ngle mesure. 5., 6., 7.,, Find eh lettered ngle mesure. 150 d d onstrut n equingulr qudrilterl tht is not regulr. isovering Geometr rtie Your Skills HT Ke urriulum ress

3 Lesson 5.3 Kite nd Trpezoid roperties me eriod te In erises 1 4, find eh lettered mesure. 1. erimeter , , 4., erimeter S 220. S S L T 4 K In erises 7 nd 8, use the properties of kites nd trpezoids to onstrut eh figure. Use ptt pper or ompss nd strightedge. 7. onstrut n isoseles trpezoid given se,, nd distne etween ses XY. X Y 8. onstrut kite with,, nd. 9. Write prgrph or flowhrt proof of the onverse of the Isoseles Trpezoid onjeture. Hint: rw prllel to T with on T. Given: Trpezoid T with T T T 34 HT 5 isovering Geometr rtie Your Skills 2008 Ke urriulum ress

4 Lesson 5.4 roperties of idsegments me eriod te In erises 1 3, eh figure shows midsegment. 1.,, 2.,, 3.,, z z z z X, Y, nd Z re midpoints. erimeter 132, 55, nd Z 20. erimeter XYZ ZX Z Y X 5. is the midsegment. Find the oordintes of nd. Find the slopes of nd. 6. plin how to find the width of the lke from to using tpe mesure, ut without using ot or getting our feet wet. (20, 10) Lke (4, 2) (9, 6) 7.,, nd re midpoints. Wht tpe of qudrilterl is? How do ou know? Give flowhrt proof showing tht. 8. Give prgrph or flowhrt proof. Given: with F FH H nd G GI I HI FG H F I G isovering Geometr rtie Your Skills HT Ke urriulum ress

5 Lesson 5.5 roperties of rllelogrms me eriod te In erises 1 7, is prllelogrm. 1. erimeter 2. 11, nd erimeter m,, 15 m ,, 5. erimeter 119, nd 6.,, erimeter ll is struk t the sme instnt two fores, F 1 nd F 2. Show the resultnt fore on the ll F 2 F 1 9. Find eh lettered ngle mesure. d e f g h i j k g 26 f G 81 h e d i j F k 10. onstrut prllelogrm with digonls nd. Is our prllelogrm unique? If not, onstrut different (nonongruent) prllelogrm. 36 HT 5 isovering Geometr rtie Your Skills 2008 Ke urriulum ress

6 Lesson 5.6 roperties of Speil rllelogrms me eriod te 1. S is retngle nd 2. KL is squre nd 3. is rhomus, S , nd 6. m KL m S m L erimeter KL m S K L In erises 4 11, mth eh desription with ll the terms tht fit it.. Trpezoid. Isoseles tringle. rllelogrm d. homus e. Kite f. etngle g. Squre h. ll qudrilterls 4. igonls iset eh other. 6. igonls re ongruent. 8. pposite sides re ongruent. 10. oth digonls iset ngles. 5. igonls re perpendiulr. 7. esures of interior ngles sum to pposite ngles re ongruent. 11. igonls re perpendiulr isetors of eh other. In erises 12 nd 13, grph the points nd determine whether is trpezoid, prllelogrm, retngle, or none of these. 12. ( 4, 1), (0, 3), (4, 0), ( 1, 5) 13. (0, 3), ( 1, 2), ( 3, 4), ( 2, 1) onstrut retngle with digonl nd. isovering Geometr rtie Your Skills HT Ke urriulum ress

7 Lesson 5.7 roving udrilterl roperties me eriod te Write or omplete eh flowhrt proof. 1. Given: is prllelogrm nd nd iset eh other Flowhrt roof Given Given nd iset eh other efinition of iset I onjeture 2. Given: rt with nd 3. Show tht the digonls of rhomus divide the rhomus into four ongruent tringles. Given: homus 4. Given: rllelogrm, Y, X X Y X Y 38 HT 5 isovering Geometr rtie Your Skills 2008 Ke urriulum ress

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