Lesson 4.1 Triangle Sum Conjecture
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1 Lesson 4.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q 2., 3., p 98 q r, s, 5., 6. t t s r s 8. m 9. m s m c c 10. Find the mesure of. 11. Find the sum of the mesures of the mrked ngles. 12. Use the digrm to eplin wh 13. Use the digrm to eplin wh nd re complementr. m m m m. 24 H 4 iscovering Geometr rctice Your kills 2008 Ke urriculum ress
2 Lesson 4.2 roperties of sosceles ringles Nme eriod te n ercises 1 3, find the ngle mesures. 1. m 2. m G N G n ercises 4 6, find the mesures. 4. m, perimeter 5. he perimeter of L 6. he perimeter of is of is 536 m. L, 344 cm. m, m 7 cm cm m L m 31 cm Nme the ngle(s) congruent to.. Nme the ngle(s) congruent to. c. Wht cn ou conclude out nd? Wh? 8., 9. nd. 10. Use the digrm to eplin f m 120, wht is wh is isosceles. m? iscovering Geometr rctice Your kills H Ke urriculum ress
3 Lesson 4.3 ringle nequlities Nme eriod te n ercises 1 nd 2, 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 sketch demonstrting wh it is not possile cm, 30 cm, 45 cm 2. 9 km, 17 km, 28 km 3. 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 ercises 4 6, rrnge the unknown mesures in order from gretest to lest c c c 40 d Wht s wrong with this picture? plin wh is isosceles. n ercises 11 nd 12, use compss nd strightedge to construct tringle with the given sides. f it is not possile, eplin wh not H 4 iscovering Geometr rctice Your kills 2008 Ke urriculum ress
4 Lesson 4.4 re here ongruence hortcuts? Nme eriod te n ercises 1 3, nme the conjecture tht leds to ech congruence JN 3. isects,, nd n ercises 4 9, nme tringle congruent to the given tringle nd stte the congruence conjecture. f ou cnnot show n tringles to e congruent from the informtion given, write cnnot e determined nd redrw the tringles so tht the re clerl not congruent. 4. is the midpoint of 5. K is kite with K. 6. nd. K J N 6 Y K 7. N N U G n ercises 10 12, use compss nd strightedge or ptt pper nd strightedge to construct tringle with the given prts. hen, if possile, construct different (noncongruent) tringle with the sme prts. f it is not possile, eplin wh not Y U U iscovering Geometr rctice Your kills H Ke urriculum ress
5 Lesson 4.5 re here ther ongruence hortcuts? Nme eriod te n ercises 1 6, nme tringle congruent to the given tringle nd stte the congruence conjecture. f ou cnnot show n tringles to e congruent from the informtion given, write cnnot e determined nd eplin wh VW 3. V W Y 4. is the ngle isector 5. N 6. FGH is prllelogrm. of. G. L K G F N L H 7. he perimeter of is 350 cm. 8. he perimeter of UV is 95 cm. s L? plin. s UV WV? plin. L U V W n ercises 9 nd 10, construct tringle with the given prts. hen, if possile, construct different (noncongruent) tringle with the sme prts. f it is not possile, eplin wh not H 4 iscovering Geometr rctice Your kills 2008 Ke urriculum ress
6 Lesson 4.6 orresponding rts of ongruent ringles Nme eriod te 1. Give the shorthnd nme for ech of the four tringle congruence conjectures. n ercises 2 5, use the figure t right to eplin wh ech congruence is true. WY is prllelogrm. Y 2. W Y 3. W Y W 4. W Y 5. W Y For ercises 6 nd 7, mrk the figures with the given informtion. o demonstrte whether the segments or the ngles indicted re congruent, determine tht two tringles re congruent. hen stte which conjecture proves them congruent. 6. is the midpoint of W nd 7. is isosceles nd is the isector Y. s YW? Wh? of the verte ngle. s? Wh? Y W n ercises 8 nd 9, use the figure t right to write prgrph proof for ech sttement. 8. F 9. F F 10. is n isosceles trpezoid with nd. Write prgrph proof eplining wh. iscovering Geometr rctice Your kills H Ke urriculum ress
7 Lesson 4.7 Flowchrt hinking Nme eriod te omplete the flowchrt for ech proof. 1. Given: nd how: Flowchrt roof Given 2. Given: Kite K with K K how: K isects K nd K Flowchrt roof K K K K K is kite K efinition of isect 3. Given: is prllelogrm how: Flowchrt roof is prllelogrm efinition of me segment 30 H 4 iscovering Geometr rctice Your kills 2008 Ke urriculum ress
8 Lesson 4.8 roving pecil ringle onjectures Nme eriod te n ercises 1 3, use the figure t right. 1. is medin, perimeter 60, nd is n ngle isector, nd m 54. m 3. is n ltitude, perimeter 42, m 38, nd 8. m, 4. U is equilterl. 5. NG is equingulr m nd perimeter NG 51. N 6. is equilterl, is isosceles with se, perimeter 66, nd perimeter 82. erimeter 7. omplete flowchrt proof for this conjecture: n n isosceles tringle, the ltitude from the verte ngle is the medin to the se. Given: sosceles with nd ltitude how: is medin Flowchrt roof is n ltitude nd re right ngles efinition of ltitude Given 8. Write flowchrt proof for this conjecture: n n isosceles tringle, the medin to the se is lso the ngle isector of the verte ngle. Given: sosceles with nd medin how: isects iscovering Geometr rctice Your kills H Ke urriculum ress
Lesson 4.1 Triangle Sum Conjecture
Lesson.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q., 3., 31 8 p 98 q 8 53 17 79 3 50. r, s, 5.,. t t 85 s 100 r 30 100 7 31 7. s 8. m 9. m s 7 35 m c c 10. Find
Lesson 4.1 Triangle Sum Conjecture
Lesson 4.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q 2., y 3., b 31 82 p 98 q 28 53 y 17 79 23 50 b 4. r, s, 5., y 6. y t t s r 100 85 100 y 30 4 7 y 31 7. s 8.
Lesson 4.1 Triangle Sum Conjecture
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
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