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7th Grade Math 2D Geometry

7th Grade Math 2D Geometry. Table of Contents. Determining if a Triangle is Possible. Scale Drawings. Special Pairs of Angles. Similar Figures. Perimeter. Click on a topic to go to that section. Area & Circumference of a of Circle. Area of Rectangles. Area of Parallelograms.

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7th Grade Math 2D Geometry

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  1. 7th Grade Math 2D Geometry

  2. Table of Contents Determining if a Triangle is Possible Scale Drawings Special Pairs of Angles Similar Figures Perimeter Click on a topic to go to that section Area & Circumference of a of Circle Area of Rectangles Area of Parallelograms Area of Triangles Area of Trapezoids Mixed Review Area of Irregular Figures Area of Shaded Regions Common Core: 7.G.1, 7.G.2, 7.G.4-6, 7.EE.3

  3. Scale Drawings Return to Table of Contents

  4. Scale drawings are used to represent objects that are either too large or too small for a life size drawing to be useful. Examples: A life size drawing of an ant or an atom would be too small to be useful. A life size drawing of the state of New Jersey or the Solar System would be too large to be useful.

  5. A scale is always provided with a scale drawing. • The scale is the ratio: drawing real life (actual) • When solving a problem involving scale drawings you should: • Write the scale as a ratio • Write the second ratio by putting the provided • information in the correct location (drawing on • top & real life on the bottom) • Solve the proportion

  6. Example: This drawing has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.

  7. Example: The distance between Philadelphia and San Francisco is 2,950 miles. You look on a map and see the scale is 1 inch : 100 miles. What is the distance between the two cities on the map? drawing 1 actual 100 Write the scale as a ratio _1 x 100 2950 100x = 2950 x = 29.5 29.5 inches on the map = =

  8. Try This: On a map, the distance between your town and Washington DC is 3.6 inches. The scale is 1 inch : 55 miles. What is the distance between the two cities?

  9. 74 On a map with a scale of 1 inch =100 miles, the distance between two cities is 7.55 inches. If a car travels 55 miles per hour, about how long will it take to get from one city to the other. 13 hrs 45 min. A B 14 hrs 30 min. 12 hrs C D 12 hrs 45 min.

  10. 75 On a map, the scale is 1/2 inch= 300 miles. Find the actual distance between two stores that are 5 1/2 inches apart on the map. 3000 miles A B 2,727 miles 3,300 miles C 1,650 miles D

  11. 76 The figure is a scale of the east side of a house. In the drawing, the side of each square represents 4 feet. Find the width and height of the door. 4 ft by 9 ft A B 4 ft by 12 ft 4 ft by 8 ft C D 4 ft by 10 ft

  12. 77 The distance between Moorestown, NJ and Duck, NC is 910 miles. What is the distance on a map with a scale of 1 inch to 110 miles?

  13. 78 The distance between Philadelphia and Las Vegas is 8.5 inches on a map with a scale 1.5 in : 500 miles . What is the distance in miles?

  14. 79 You are building a room that is 4.6 m long and 3.3 m wide. The scale on the architect's drawing is 1 cm : 2.5 m. What is the length of the room on the drawing?

  15. 80 You are building a room that is 4.6 m long and 3.3 m wide. The scale on the architect's drawing is 1 cm : 2.5 m. What is the width of the room on the drawing?

  16. 81 Find the length of a 72 inch wide wall on a scale drawing with a scale 1 inch : 2 feet.

  17. 82 You recently purchased a scale model of a car. The scale is 15 cm : 10 m. What is the length of the model car if the real car is 4 m?

  18. 83 You recently purchased a scale model of a car. The scale is 15 cm : 10 m. The length of the model's steering wheel is 1.25 cm. What is the actual length of the steering wheel?

  19. Similar Figures Return to Table of Contents

  20. Two objects are similar if they are the same shape but different sizes. • In similar objects: • corresponding angles are congruent • corresponding sides are proportional

  21. To check for similarity: • Check to see that corresponding angles are congruent • Check to see that corresponding sides are proportional • (Cross products are equal)

  22. Example: Is the pair of polygons similar? Explain your answer. 4 3_ 6 4.5 4(4.5) = 6(3) 18 = 18 YES 4 yd 3 yd 4.5 yd 6 yd 4 _6_ 3 4.5 4(4.5) = 6(3) 18 = 18 YES = = OR

  23. Example: Is the pair of polygons similar? Explain your answer. 5 8_ 10 13 5(13) = 10(8) 65 = 80 NO 8 m 5 m 13 m 10 m _5 10_ 8 13 5(13) = 8(10) 65 = 80 NO = OR =

  24. 84 Are the polygons similar? You must be able to justify your answer. (Shapes not drawn to scale.) Yes No 15 ft 9 ft 12 ft 21 ft

  25. 85 Are the polygons similar? You must be able to justify your answer. (Shapes not drawn to scale.) Yes 10 m No 2.5 m 2 m 8 m

  26. 86 Are the polygons similar? You must be able to justify your answer. (Shapes not drawn to scale.) Yes 15 yd No 37.5 yd 6 yd 15 yd

  27. Example: Find the value of x in the pair of similar polygons. 15 6 x 10 15(10) = 6x 150 = 6x 25 cm = x x 10 cm 15 cm 6 cm 8 cm 15 x 6 10 15(10) = 6x 150 = 6x 25 cm = x = = OR

  28. Try This: Find the value of y in the pair of similar polygons. 15 in 7.5 in 5 in y

  29. 87 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 80 80 y 110 110

  30. 88 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 17.5 ft 25 ft 25 ft w 18 ft

  31. 89 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) x 4 m 4.25 m 17 m

  32. 90 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) y 6 mm 11 mm 38.5 mm

  33. 91 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 7 m ? 13 m 30 m 70 m

  34. 92 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 81 m 429 m 63 m 231 m ? 297 m

  35. 93 Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 2 mm x 5 mm 27.5 mm

  36. Determining if a Triangle is Possible Return to table of contents

  37. How many different acute triangles can you draw? How many different right scalene triangles can you draw? Recall that triangles can be classified according to their side lengths and the measure of their angles. Sides: Scalene - no sides are congruent Isosceles - two sides are congruent Equilateral - all three sides are congruent Angles: Acute - all three angles are acute Right - contains one right angle Obtuse - contains one obtuse angle

  38. There is another property that applies to triangles: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What does this mean? If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. If that is not true, then it is not possible to construct a triangle with the given side lengths.

  39. Example: Determine if sides of length 5 cm, 8 cm and 12 cm can form a triangle? Test all three pairs to see if the sum is greater: 5 + 8 > 12 5 + 12 > 8 8 + 12 > 5 13 > 12 17 > 8 20 > 5 Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.

  40. Example: Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test all three pairs to see if the sum is greater: 3 + 4 > 9 3 + 9 > 4 4 + 9 > 3 7 > 9 12 > 4 13 > 3 No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.

  41. Try These: Determine if triangles can be formed with the following side lengths: 1. 4 cm, 7 cm, 10 cm 2. 24 mm, 20 mm, 30 mm 4 + 7 > 10 24 + 20 > 30 4 + 10 > 7 24 + 30 > 20 7 + 10 > 4 20 + 30 > 24 YES YES 3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in 7 + 9 = 16 9 + 13 < 24 7 + 16 > 9 9 + 24 > 13 16 + 9 > 7 13 + 24 > 9 NO NO

  42. 1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work! A Yes B No

  43. 2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work! A Yes B No

  44. 3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work! A Yes B No

  45. 4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work! A Yes B No

  46. 5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work! A Yes B No

  47. 6 A triangle could have which of the following sets of angles? A B C D

  48. 7 A triangle could have which of the following sets of angles? A B C D

  49. Example: Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft. Side 1 = 12 ft Side 2 = 16 ft The 3rd side must be less than: 12 + 16 > 3rd side 28 ft > 3rd side The 3rd side must be greater than: 12 + 3rd side > 16 3rd side > 4 The 3rd side must be greater than 4 ft and less than 28 ft.

  50. Example: Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm. Side 1 = 9 cm Side 2 = 15 cm The 3rd side must be less than: 9 + 15 > 3rd side 24 cm > 3rd side The 3rd side must be greater than: 9 + 3rd side > 15 3rd side > 6 The 3rd side must be greater than 6 cm and less than 24 cm.

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