Similar Figures & Scale Drawings

Transcription

1 Similar Figures & Scale Drawings Task Cards

2 1 10 m m 4 m The shapes are similar: What is the measure of side HG? What scale factor was used to enlarge Δ UVW to Δ KLM? The two kites are similar. What is the value of x? Find the value of x if ΔGTH ~ΔSKM Find the value of x The two triangles are similar Find the value of a? The two trapezoids are similar. What is the value of x? The two rectangles are similar. What is the value of x? The polygons above are similar.

3 If the triangles are similar, what scale factor is used from ΔABC to ΔDEF? Δ ABC ~ Δ XYZ Find the measure of side YZ Find the value of x in 50 in 40 in 64 in Find the value of x if the two shapes are similar 16 What scale factor was used to enlarge ABCD to WZYX? Given: ABCD ~ EFGH Find AD. ABCD ~ MNOP. What scale factor was used to reduce ABCD to MNOP? What is the length of side AB? What is the value of the missing side length?

4 ABC ~ DEF what is the m F? ABCD ~ FGHJ what is the m J? ABCD ~ GFEH what is the m G? 22 Y T 95 X R S Z x RST ~ XYZ what is the m Z? MNOP ~ STQR what is the m N? GHI ~ SRQ what is the value of x? w y TQRS ~ MNOP what is the value of y? What is the value of w? What is the m ABC?

5 Michele wanted to measure the height of her 28 her school s `lagpole. She placed a mirror on the ground 48 feet from the `lagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Find the height of the `lagpole The 5 ft tall person casts a shadow that is 4 ft long. How tall is the `lagpole if it casts a 28 foot shadow? What is the height of the tree? 31 What is the height of the `lagpole? meters The 6- foot man casts a shadow that is 10 feet long. If the pyramid casts a 48 feet long shadow, how tall is the pyramid? 10 meters into the pool, the depth of the water is 2 meters. How deep is th e water 38 meters into the pool?? 34 The shorter tree is 10.5 ft. tall, and casts a shadow that is feet long. If the taller tree casts a 17.5 ft. shadow, how tall is the tree? Calculate the height of the `lagpole. Calculate the distance across the pond in meters.

6 What is the value of y? What is the perimeter of triangle RST? Find the value of y What is the measure of segment EB? What is the perimeter of triangle MQR?

7 m 50 m Park Playground 4,000 m 2 48 The two rectangles are similar. Find the perimeter of the larger rectangle. 49 A school playground is similar in shape to the community park. You can mow 250 square meters of grass in 10 minutes. How many minutes would it take you to mow the playground and the park? Δ ABC ~ Δ DEF Find the perimeter of triangle ABC. 8.4 The two pictures are similar. What is the approximate area of the smaller picture? Find the value of x The distance between Iowa city and 54 Chicago on the map is 3 ⅕ cm. What is the actual distance in miles? Jack and Jill both walk from point A to point D. Jack straight past point E, and directly to point D. Jill walks down to point B, and then past point C, to get to point D. How much farther does Jill walk than Jack? What is the distance across the river? 1 cm = 25 miles

8 The picture above needs to be resized to go in a magazine. A scale factor of 0.75 will be used to calculate the new dimensions. How many square inches will the new picture cover in the magazine? 58 To the left is a scale drawing of a moose. If the actual length of the moose is 15 ¾ feet, how many feet is represented by each inch? An artist is creating an enlarged drawing of the ant above. In order to keep the drawing proportional he will use a scale of 1cm:8 in. What will the length of the drawing be? A model of the empire state building is shown to the left. If a scale of 1in:200 feet was used to build the model, what is the actual height of the building? 59 A scale of 1cm : 50 miles was used to draw the map of North Carolina above. What is the distance across North Carolina in miles? 60 A scale factor of 1.5 will be used to create an enlarged replica of the `lag above. What will the area of the new `lag be? 61 The robot below is a scale model of a real robot built to be the size of an average human. If the actual robot is 6 feet tall, and the ruler is measuring the model in inches, how many feet does 1 inch represent? 62 Martin is creating a toy model of the boat shown above. If he uses a scale of 1m = 0.4cm, what will the length of the toy model be? Brian wants to put this picture in the school newspaper in a space that is 5 inches tall. If he enlarges the picture proportionally so that it is 5 inches tall, how many square inches will it cover in the paper? 63

9 Answer key Page 1: 1.) 5m 2.) 1⅓ 3.) 40 cm. 4.) 4 cm 5.) 6⅔ u 6.) 10 u 7) 18⅔ u 8.) 16.5 u 9.) 14 u Page 2: 10.) ) in 12.) 8u 13.) 21 in 14.) ) 62.5 in. 16.) ⅔ 17.) 6cm 18.) 13.2 u Page 3: 19.) ) ) ) ) ) x = 7 25.) y = 9 26.) ) w = 3.5 Page 4: 28.) 20 ft. 29.) 35 ft. 30.) 3.3 m 31.) 32.4 ft 32.) 28.8 ft. 33.) 7.6 m 3416⅓ ft 35.) 51 ft. 36.) 15 m Page 5: 37.) ) ) ) ) 3 42.) ) ) ) 45 Page 6: 46.) cm 47.) 200 min 48.) ) 30yd 50.) 3.9 in 2 51.) x = ) 25.8 u 53.) 90 m 54.) 80 miles Page 7: 55.) 27 in 2 56.) 22 in 57.) 525 miles 58.) 5.25ft 59.) 1,260 ft 60.) in 2 61.) ¾ foot 62.) 48 cm 63.) 12.5 in 2

10 Page 1 Answer Bank: 1⅓ 40 18⅔ Page 2 Answer Bank: ⅕ 9¾ ⅔ ⅔ ⅘ Page 3 Answer Bank: Page 4 Answer Bank: ⅓ Page 5 Answer Bank: Page 6 Answer Bank: Page 7 Answer Bank: ¾ ,