Lesson 4.1 ringle um onjeture me eriod te n erises 1 9, determine the ngle mesures. 1. p, q 2., 3., 31 82 p 98 q 28 53 17 79 23 50 4. r, s, 5., 6. t t s r 100 85 100 30 4 7 31 7. s 8. m 9. m s 76 35 m 10. plin wh nd 11. Find the sum of the 12. plin wh re omplementr. mesures of the mrked m m ngles. m m. 13. Find the mesure of. 14. n isoseles the mesure of verte is 80. f is the inenter of the tringle, wht is the mesure of? isovering eometr rtie our kills H 4 23 2003 Ke urriulum ress
Lesson 4.2 roperties of peil ringles me eriod te n erises 1 3, find the ngle mesures. 1. m 2. m 3. 110 58 4.. me the ngle(s) ongruent to.. me the segment(s) ongruent to. 5.. me the ngle(s) ongruent to.. me the ngle(s) ongruent to.. Wht n ou onlude out nd? Wh? 6. plin wh is 7., 8. nd. isoseles. f m 120, wht is 4 m? 70 55 2 79 9. me ll ngles ongruent to in the figure t right. plin wh JH is isoseles. 10. Using ompss nd strightedge or ptt pper nd strightedge, onstrut n isoseles tringle with se ngle tht mesures 75. plin our method. n erises 11 nd 12, find the missing oordintes. F J H 11. 12. (, ) (, 6) (5, 2) (9, 2) ( 5, 1) (1, ) 24 H 4 isovering eometr rtie our kills 2003 Ke urriulum ress
Lesson 4.3 ringle nequlities me eriod te n erises 1 4, determine whether it is possile to drw tringle with sides of the given mesures. f it is possile, write es. f it is not possile, write no nd mke sketh demonstrting wh it is not possile. 1. 16 m, 30 m, 45 m 2. 9 km, 17 km, 28 km 3. 32 in., 60 in., 87 in. 4. 13.4 ft, 17.7 ft, 31.1 ft n erises 5 nd 6, use ompss nd strightedge to onstrut tringle with the given sides. f it is not possile, eplin wh not. 5. 6. 7. f 17 nd 36 re the lengths of two sides of tringle, wht is the rnge of possile vlues for the length of the third side? n erises 8 13, rrnge the unknown mesures in order from gretest to lest. 8. 9. 10. 32 13 18 61 20 48 d e 11. 12. 13. 71 28 40 d 30 90 88 14. 15. 16. Wht s wrong with this piture? 142 66 158 160 120 17. plin wh is isoseles. 18. plin wh the sum of the three ltitudes of tringle is lws less thn its perimeter. 2 isovering eometr rtie our kills H 4 25 2003 Ke urriulum ress
Lesson 4.4 re here ongruene hortuts? me eriod te n erises 1 3, use ompss nd strightedge or ptt pper nd strightedge to onstrut tringle with the given prts. hen, if possile, onstrut different (nonongruent) tringle with the sme prts. f it is not possile, eplin wh not. 1. 2. 3. U U n erises 4 6, nme the onjeture tht leds to eh ongruene. 4. 5. J 6. isets,, nd n erises 7 11, use the informtion given to omplete eh sttement. f the tringles nnot e shown to e ongruent from the informtion given, write nnot e determined nd redrw the figures to show tht the tringles re lerl not ongruent. o not ssume tht segments or ngles re ongruent just euse the pper to e ongruent. 7. is the midpoint of 8. K is kite with K. 9. nd. K 10. O 11. 12. O O. Find the oordintes of nd. O 6 K 8 9 9 8 J 6 U O (5, 7) (1, 5) (7, 3) 26 H 4 isovering eometr rtie our kills 2003 Ke urriulum ress
Lesson 4.5 re here Other ongruene hortuts? me eriod te 1. Use ompss nd strightedge or ptt pper nd strightedge to onstrut from the given prts. How does our tringle ompre to the tringle onstruted others in our lss? plin. 2. Use ompss nd strightedge or ptt pper nd strightedge to onstrut. plin our proedure. Wht onjeture tells ou tht our tringle is ongruent to the tringle of nother student? n erises 3 8, use the informtion given to omplete eh sttement. f the tringles nnot e shown to e ongruent from the informtion given, write nnot e determined nd redrw the figures to show tht the tringles re lerl not ongruent. o not ssume tht segments or ngles re ongruent just euse the pper to e ongruent. 3. 4. VW 5. O V W 6. is the ngle isetor 7. 8. FH is prllelogrm. of.. L 9. me three pirs of ongruent tringles. 10.. Find the oordintes For eh pir, eplin how ou know of nd. how tht. the re ongruent. (5, 9) (8, 13) (15, 5) F K L H (10, 3) isovering eometr rtie our kills H 4 27 2003 Ke urriulum ress
Lesson 4.6 orresponding rts of ongruent ringles me eriod te 1. ive the shorthnd nme for eh of the four tringle ongruene onjetures. n erises 2 nd 3, use the figures t right to eplin wh eh ongruene is true. 2. 3. n erises 4 7, use the figure t right to eplin wh eh ongruene is true. W is prllelogrm. 4. W 5. W 6. W 7. W For erises 8 nd 9, op the figures onto our pper nd mrk them with the given informtion. o demonstrte whether or not the segments or the ngles indited re ongruent, determine tht two tringles re ongruent. hen, stte whih onjeture proves them ongruent. 8. is the midpoint of W nd 9. is isoseles nd is the isetor. s W? Wh? of the verte ngle. s? Wh? W W n erises 10 nd 11, use the figure t right to write prgrph proof for eh sttement. 10. F 11. F 12. is n isoseles trpezoid with nd. Write prgrph proof eplining wh. F 28 H 4 isovering eometr rtie our kills 2003 Ke urriulum ress
Lesson 4.7 Flowhrt hinking me eriod te omplete or write flowhrt for eh proof. 1. iven: nd how: Flowhrt roof iven 2. iven: Kite K with K K how: K isets K nd K Flowhrt roof K K K K K is kite K efinition of iset 3. iven: is prllelogrm how: Flowhrt roof is prllelogrm efinition of me segment isovering eometr rtie our kills H 4 29 2003 Ke urriulum ress
Lesson 4.8 roving soseles ringle onjetures me eriod te n erises 1 3, use the figure t right. is isoseles with. 1. is medin, perimeter 60, nd 22. 2. is n ngle isetor, nd m 54. m 3. is n ltitude, perimeter 55, m 19, nd 8. m, 4. U is equilterl. 5. is equingulr nd perimeter m 51. U 6. is equilterl, is isoseles with se, perimeter 66, nd perimeter 82. erimeter 7. omplete flowhrt proof for this onjeture: n n isoseles tringle, the ltitude from the verte ngle is the medin to the se. iven: soseles with nd ltitude how: is medin Flowhrt roof is n ltitude nd re right ngles efinition of ltitude iven 8. Write flowhrt proof for this onjeture: n n isoseles tringle, the medin to the se is lso the ngle isetor of the verte ngle. 30 H 4 isovering eometr rtie our kills 2003 Ke urriulum ress