Lesson 5.1 Polygon Sum Conjecture
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1 Lesson 5.1 Polgon Sum onjeture In Eerise 1, find eh lettered ngle mesure. 1.,,, d, e e d ne eterior ngle of regulr polgon mesures 10. Wht is the mesure of eh interior ngle? How mn sides does the polgon hve? 3. The sum of the mesures of the interior ngles of regulr polgon is How mn sides does the polgon hve? 4. is squre. E is n equilterl tringle. E 32 HPTER 5 isovering Geometr Prtie Your Skills 2008 Ke urriulum Press
2 Lesson 5.2 Eterior ngles of Polgon 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 Eerise 5, find eh lettered ngle mesure. 5., isovering Geometr Prtie Your Skills HPTER Ke urriulum Press
3 Lesson 5.3 Kite nd Trpezoid Properties In Eerises 1 4, find eh lettered mesure. 1. Perimeter , , 4., Perimeter PQRS 220. PS S 4 1 R 2 3 P T 4 Q 34 HPTER 5 isovering Geometr Prtie Your Skills 2008 Ke urriulum Press
4 Lesson 5.4 Properties of Midsegments In Eerises 1 3, eh figure shows midsegment. 1.,, 2.,, 3.,, z z z z MN is the midsegment. Find the oordintes of M nd N. Find the slopes of nd MN. M (20, 10) (4, 2) N (9, 6) isovering Geometr Prtie Your Skills HPTER Ke urriulum Press
5 Lesson 5.5 Properties of Prllelogrms In Eerises 1 7, is prllelogrm. 1. Perimeter 2. 11, nd Perimeter m,, 15 m ,, 5. Perimeter 119, nd 6.,, Perimeter Find eh lettered ngle mesure. g h h G 81 d e f i j k g 26 f e d i E j F k 36 HPTER 5 isovering Geometr Prtie Your Skills 2008 Ke urriulum Press
6 Lesson 5.6 Properties of Speil Prllelogrms 1. PQRS is retngle nd 2. KLMN is squre nd 3. is rhomus, S 16. NM 8. 11, nd 6. Q m KL m QRS m ML PR Perimeter KLMN m S R N M P Q K L In Eerises 4 11, mth eh desription with ll the terms tht fit it.. Trpezoid. Isoseles tringle. Prllelogrm d. Rhomus e. Kite f. Retngle 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. Mesures of interior ngles sum to pposite ngles re ongruent. 11. igonls re perpendiulr isetors of eh other. In Eerises 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) isovering Geometr Prtie Your Skills HPTER Ke urriulum Press
7 Lesson 5.7 Proving Qudrilterl Properties Write or omplete eh flowhrt proof. Q 1. Given: is prllelogrm nd P Q R Show: nd PQ iset eh other Flowhrt Proof P PR QR R Given Given PR nd QP iset eh other efinition of iset I onjeture 2. Given: rt with nd Show: 3. Show tht the digonls of rhomus divide the rhomus into four ongruent tringles. Given: Rhomus Show: 4. Given: Prllelogrm, Y, X Show: X Y X Y 38 HPTER 5 isovering Geometr Prtie Your Skills 2008 Ke urriulum Press
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