Applications. A rigt triangle as legs of lengt inces and inces. a. Find te area of a square drawn on te ypotenuse of te triangle. b. Wat is te lengt of te ypotenuse?. Use te Pytagorean Teorem to find te lengt of te ypotenuse of tis triangle. c 3 cm For: Help wit Eercise Web Code: ape-30 6 cm 3. On dot paper, find two points tat are!7 units apart. Label te points W and X. Eplain ow you know te distance between te points is!7 units.. On dot paper, find two points tat are!0 units apart. Label te points Y and Z. Eplain ow you know te distance between te points is!0 units. Find te missing lengt(s).. 6. 3 in. k 3 cm in. 8 cm 7. 7 m m m y 38 Looking for Pytagoras
For Eercises 8, use te map of Euclid. Find te flying distance in blocks between te two landmarks witout using a ruler. Eplain. 8. greenouse and stadium 9. police station and art museum 0. greenouse and ospital. City Hall and gas station N y Gas station 3 Stadium Greenouse City Hall 7 6 3 3 6 7 Art museum Animal selter 3 Hospital Police station Cemetery. Multiple Coice Refer to te map above. Wic landmarks are!0 blocks apart? A. greenouse and stadium B. City Hall and art museum C. ospital and art museum D. animal selter and police station Investigation 3 Te Pytagorean Teorem 39
3. Te diagram at te rigt sows a rigt triangle wit a square on eac side. a. Find te areas of te tree squares. b. Use te areas from part (a) to sow tat tis triangle satisfies te Pytagorean Teorem.. Sow tat tis triangle satisfies te Pytagorean Teorem.. Multiple Coice Coose te set of side lengts tat could make a rigt triangle. F. 0 cm, cm, 6 cm G. cm, 6 cm, 0 cm H. cm, 0 cm,!0 cm J. 8 cm, 9 cm, cm Tell weter te triangle wit te given side lengts is a rigt triangle. 6. 0 cm, 0 cm,!00 cm 7. 9 in., 6 in., in. For: Multiple-Coice Skills Practice Web Code: apa-3 Connections 8. Te prism at te rigt as a base tat is a rigt triangle. a. Wat is te lengt of a? b. Do you need to know te lengt of a to find te volume of te prism? Do you need to know it to find te surface area? Eplain.. cm 6 cm a cm c. Wat is te volume? d. Wat is te surface area? e. Sketc a net for te prism. 0 Looking for Pytagoras
For Eercises 9, refer to te figures below. r r w w Cylinder Cone Prism Pyramid 9. Multiple Coice Wic epression represents te volume of te cylinder? A. pr + pr B. pr C. D. pr 3 pr 0. Multiple Coice Wic epression represents te volume of te cone? F. pr + pr G. pr H. J. pr 3 pr. Multiple Coice Wic epression represents te volume of te prism? A. (Ow + O + w) B. Ow C. Ow D. Ow 3. Multiple Coice Wic epression represents te volume of te pyramid? F. (Ow + O + w) G. Ow H. Ow J. Ow 3 3. In te city of Euclid, Hilary s ouse is located at (, -3), and Jamilla s ouse is located at (, -). a. Witout plotting points, find te sortest driving distance in blocks between te two ouses. b. Wat is te eact flying distance between te two ouses? Investigation 3 Te Pytagorean Teorem
. Wic labeled point is te same distance from point A as point B is from point A? Eplain. G C J B F A D H E. In te drawing at rigt, te cone and te cylinder ave te same eigt and radius. Suppose te radius r of te cone is units and te slant eigt d is!9 units. a. Wat is te eigt of te cone? b. Wat is te volume of te cone? r d 6. In te drawing below, te pyramid and te cube ave te same eigt and base. a. Suppose te edge lengt of te cube is 6 units. Wat is te volume of te pyramid? b. Suppose te edge lengt of te cube is units. Wat is te volume of te pyramid? Looking for Pytagoras
Etensions 7. Any tilted segment tat connects two dots on dot paper can be te ypotenuse of a rigt triangle. You can use tis idea to draw segments of a given lengt. Te key is finding two square numbers wit a sum equal to te square of te lengt you want to draw. For eample, suppose you want to draw a segment wit lengt! units. You can draw a rigt triangle in wic te sum of te areas of te squares on te legs is. Te area of te square on te ypotenuse will be square units, so te lengt of te ypotenuse will be! units. Because and are square numbers, and + =, you can draw a rigt triangle wit legs of lengts and. a. To use tis metod, it elps to be familiar wit sums of square numbers. Copy and complete te addition table to sow te sums of pairs of square numbers. 9 6 36 9 6 9 6 36 9 6 For parts (b) (d) find two square numbers wit te given sum. b. 0 c. d. 89 For parts (e) (), draw tilted segments wit te given lengts on dot paper. Use te addition table to elp you. Eplain your work. e.!6 units f. 0 units g.!0 units.!0 units Investigation 3 Te Pytagorean Teorem 3
For Eercises 8 33, tell weter it is possible to draw a segment of te given lengt by connecting dots on dot paper. Eplain. 8.! units 9.!3 units 30.! units 3.! units 3.!6 units 33.!7 units 3. Ryan looks at te diagram below. He says, If te center of tis circle is at te origin, ten I can figure out te radius. y (3, ) O a. Eplain ow Ryan can find te radius. b. Wat is te radius? 3. Use te grap to answer parts (a) (c). 0 y 8 K L M 6 0 0 J 6 8 0 a. Find te coordinates of J and K. b. Use te coordinates to find te distance from J to K. Eplain your metod. c. Use your metod from part (b) to find te distance from L to M. Looking for Pytagoras