Answer Key Lesson 6: Workshop: Angles and Lines

Transcription

1 nswer Key esson 6: tudent Guide ngles nd ines Questions 1 3 (G p. 406) ; hey re the sme Here re four different ptterns tht re used to mke quilts. Work with your group. se your Power Polygons to mke these ptterns. whirligig wheel hexgon Ferris wheel ptchwork hese ptterns re clled tesselltions ptterns mde from one or more shpes tht do not overlp, leve no gps, nd tht cn repet over nd over. he following picture shows tesselltion mde entirely of hexgons. lrge dot is plced where three hexgons come together. We cll this vertex of the tesselltion. 1. Wht is the ngle mesure of ech of the corners of the three hexgons where they come together? Wht is the sum of the three ngles? 2. hoose nother vertex. re the ngles t your new vertex the sme s those t the lrge dot in the drwing bove? 3. Find the sum of the ngles t the new vertex. se the Prctice with ngles nd ines pges in the tudent ctivity ook to prctice the concepts in this unit. 406 G Grde 4 nit 9 esson 6 tudent Guide - Pge 406 G Grde 4 nit 9 esson 6 nswer Key 1

2 nswer Key esson 6: Prctice with ngles nd ines ngles elf-heck: Questions stimte the size of these ngles using the benchmrks 0º, 90º, nd 180º. Write your estimte ner the ngle. 2. Grce drew n ngle of 75º.. Wht kind of ngle did Grce drw?. If she drws n ngle tht is exctly 15 lrger, wht kind of ngle is it?. he wnts to drw n obtuse ngle. Her obtuse ngle will hve to be t lest how mny degrees lrger thn her first ngle? se the elf-heck Questions nd the menu to choose prctice. Working On It! Getting It! Got It! I could use I just need I m redy n I o his? some extr more some for help.. prctice. chllenge stimte the size of n ngle using g benchmrks: 90º, 180º, nd 360º. Know the difference between cute, obtuse, nd right ngles. Q# 3 6 Q# 5 8 Q# 7 8 Grde 4 nit 9 esson tudent ctivity ook - Pge stimte the size of the ngles below using the benchmrks 0º, 90º, nd 180º. For exmple, sy little lrger thn 90º, or very close to 90º, or estimte in degrees, such s º 90º 180º bel ech ngle in Question 3 s cute, right, or obtuse. 5. Without mesuring, identify these ngles s cute, right, or obtuse..... hoose one nd explin how you decided. tudent ctivity ook Prctice with ngles nd ines Questions 1 26 ( pp ) 1. Possible response: close to 180 or 170 ; close to 90 or n cute ngle. right ngle. t lest 16 lrger 3. Responses nd estimtes will vry.. etween 90 nd 180, or bout 120. Very close to 180, or bout 170. Very close to 0, or bout 20. little smller thn 90, or bout obtuse. obtuse. cute. cute 5.. obtuse. obtuse. right. cute Possible response for : I used the corner of piece of pper nd both edges mtched. I knew the corner forms right ngle. 336 Grde 4 nit 9 esson 6 tudent ctivity ook - Pge G Grde 4 nit 9 esson 6 nswer Key

3 nswer Key esson 6: 6. Responses will vry; mke sure tht students estimtes re in the correct qudrnt.. round 95. round 135. round 30. round 330. round 70 F. round cute ngles include PR, PQ, PQ. Obtuse ngles include P, QPR, QP. Right ngles include VRP, R, R 8. PQ is bout 45 RPQ is bout 135 R is bout = 66. G = 144. V = 15 W = stimte the sizes of the ngles below. Give your nswers in degrees, for exmple, 30º or 90º. You my use squre corner to help you, but not protrctor. Grde 4 nit 9 esson tudent ctivity ook - Pge 337 se the figure below for Questions 7 nd 8. V R dd nd ubtrct ngles elf-heck: Question 9 9. Without using protrctor, find the missing ngle mesures.. P 24º = Q. G 7.. Identify two cute ngles. Write the ngle nmes using three letters, such s.. two obtuse ngles.. right ngle. 8. se the benchmrks 0º, 90º, nd 180º to estimte the size of the following ngles. PQ is RPQ is R is 338 Grde 4 nit 9 esson 6 tudent ctivity ook - Pge º G = F n I o his? V W 60º dd nd subtrct ngle mesures. s. Q# 10 11, 13, 15 V = 90 V = VW V = W = se the elf-heck Question nd menu to choose prctice. Working On It! Getting It! Got It! I could use I just need I m redy some extr some more for help.. prctice. chllenge. Q# 11 14, 16 Q# 12 14, 17 Grde 4 nit 9 esson tudent ctivity ook - Pge 339 G Grde 4 nit 9 esson 6 nswer Key 3

4 nswer Key esson 6: 10. se protrctor to mesure the ngles =. =. =. Is this sttement true? xplin. = FG is right ngle. Without using protrctor, find the mesure of FH. K = O. Without using protrctor, find the ngle mesure of KO. K O Grde 4 nit 9 esson 6 20º F H 12 G 10.. = 70. = 20. = 90. Yes; he sum of the smller ngles is equl to the mesure of the lrger ngle. 11. FH = KO = = 20 = 150 = 10. he sum is ee shpe on pge.. 4 pieces. Right ngles. 90 ech. 360 tudent ctivity ook - Pge esure the ngles in ringle Wht is the sum of, nd? Rectngle is built from three tringles. =. Without using protrctor, find the mesures of the ngles below. Write the mesures ner the ngle.. =. =. =. = 20º 15.. ke the shpe with solid lines using your power polygons. se the yellow squre () nd lrge green tringle (). If you hve enough pieces, you cn mke the whole shpe in the dotted lines.. Find the dot on your shpe. How mny pieces come together t the dot?. re the ngles t the dot cute, obtuse, or right?. stimte nd then mesure the size of the ngle of ech piece t the dot.. dd ll the ngle mesures t the dot. Wht is the sum of ll the ngle mesures? Grde 4 nit 9 esson Grde 4 nit 9 esson 6 tudent ctivity ook - Pge 341 tudent ctivity ook - Pge G Grde 4 nit 9 esson 6 nswer Key

5 nswer Key esson 6: 16.. ee shpe on pge.. 4 pieces. One ngle is cute, two re right, nd one is obtuse.. he ngle of the smll green tringle is 60, the ngles of the squres re 90, nd the ngle of the hexgon is ee shpe on pge.. 4 pieces. wo re obtuse, two re cute.. he ngles of the green tringles re 60, the ngles of the red trpezoids re F. 3 pieces G. One ngle is cute, one is obtuse, nd one is stright. H. he stright ngle from the red trpezoid is 180, the obtuse ngle from the other red trpezoid is 120, the cute ngle from the green tringle is 60. I ke the prt of the shpe with solid lines using your power polygons. se ornge squres (), yellow hexgons (H), nd smll green tringles (). If you hve enough pieces, you cn extend the shpe s shown with dotted lines.. Find the dot on your shpe. How mny pieces come together t the dot?. re the ngles t the dot cute, obtuse, or right?. stimte nd then mesure the size of the ngle of ech piece t the dot.. dd ll the ngle mesures t the dot. Wht is the sum of ll the ngle mesures? Grde 4 nit 9 esson tudent ctivity ook - Pge ke the shpe with the solid lines using your power polygons. se smll green tringles () nd red trpezoids (K). If you hve enough pieces, you cn extend the shpe s shown with dotted lines.. Find the dot on your shpe. How mny pieces come together t the dot?. re the ngles cute, obtuse, or right?. stimte nd then mesure the size of the ngle of ech piece t the dot dd ll the ngle mesures t the dot. Wht is the sum of ll the ngle mesures? F. ow find the squre on your shpe. How mny pieces touch t the squre? G. re the ngles cute, obtuse, or right? Or is there nother kind of ngle? Wht is it? H. stimte nd then mesure the size of the ngle of ech piece t the squre. I. dd ll the ngle mesures. Wht is the sum of ll the ngle mesures t the squre? Grde 4 nit 9 esson 6 tudent ctivity ook - Pge 344 G Grde 4 nit 9 esson 6 nswer Key 5

6 nswer Key esson 6: ines elf-heck: Questions one set of prllel lines.. two lines tht re perpendiculr to ech other ry on the figure.. line segment on the figure.. Find nd nme qudrilterl on the figure. 20. se protrctor to drw line perpendiculr to V. 21. se protrctor to drw line prllel to V. se the elf-heck Questions nd menu to choose prctice. Working On It! Getting It! Got It! I could use I just need I m redy n I o his? some extr some more for help.. prctice. chllenge. rw nd identify lines tht intersect, re perpendiculr, r, or re prllel. Q# Q# Q# Grde 4 nit 9 esson tudent ctivity ook - Pge he figure below is n octgon becuse it hs 8 sides. ch side is prt of line which mens ech side is line segment. nd, PR. Possible responses include VR nd PR, R nd 19.. Possible responses include RV, V, R, 18.. Possible responses include R nd Q Possible responses include P, R, Q,. PRQ Q P 22.. FGH, HGF, ny sequence tht is in order round the octgon is cceptble.. Possible responses include nd F nd GF, nd GH, nd H. hey intersect, nd right ngle is formed t the intersection. he lines re perpendiculr. V R,. Wht re two different wys you cn nme this octgon?. 4 pirs of prllel lines tht mke up the octgon.. se your ruler to drw line segment from Point to Point H. rw nother line segment from Point to Point F. o H nd F intersect? Wht kind of ngle is formed t the intersection? Wht cn you sy bout H nd F? H G F 346 Grde 4 nit 9 esson 6 tudent ctivity ook - Pge G Grde 4 nit 9 esson 6 nswer Key

7 nswer Key esson 6: 23.. Responses will vry. Possible response shown below.. Yes, JK ngle. intersects. hey mke right 24. Responses will vry. Possible response: below. it. tht is perpendiculr to. lso intersect? If so, tell if the intersection of JK nd mkes n cute ngle, n obtuse ngle, or right ngle rw line tht is prllel to. rw line JK. oes JK W X 24.. rw line segment R tht intersects. rw but not. tht intersects nd forms n obtuse ngle. tht intersects.. rw ry WX J K R Grde 4 nit 9 esson J tudent ctivity ook - Pge cm 25.. se these clues to drw ringle JK: 26. K 8 cm. J 60, K 90, 30 (choice ) O 4 cm cm lue 1: ide JK is 6 cm long lue 2: ngle K is right ngle lue 3: ide K is 8 cm long. ook t your ringle JK. Which of the following is close to the correct ngle mesures for ringle JK? Fill in the circle by the correct letter.. J 80º, K 90º, 10º. J 125º, K 90º, 79º. J 60º, K 90º, 30º. J 20º, K 90º, 27º 26. se these clues to drw ringle O. lue 1: ngle is 120º lue 2: ngle is 30º lue 3: ide is 4 cm long 348 Grde 4 nit 9 esson 6 tudent ctivity ook - Pge 348 G Grde 4 nit 9 esson 6 nswer Key 7