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Modeling Geometric Figures

Modeling Geometric Figures. Module8: 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Module 8. Ready to go on? Page 259 Are you Ready ? Page 234

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Modeling Geometric Figures

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  1. Modeling Geometric Figures Module8: 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

  2. Module 8 • Ready to go on? Page 259 • Are you Ready? Page 234 • Vocabulary – Worksheet

  3. 8.1 Similar Shapes & Scale Drawings How can you use scale drawings to solve problems?

  4. Explore Activity 1 • As a class we will • Complete page 237 Letter A # 1-3

  5. Notes • Formula: Area of a square or rectangle • Area = length * width • A=l*w • Step 1- Figure out what the scale of the drawing is. For example, how many inches represent a foot. • Step 2 – Calculate all of the numbers between the scale drawing and the actual size. For example, the label is 3 inches on the scale how many feet is the actual wall? • Step 3 – Find the area of the actual object.

  6. Example 1 • The art class is planning to paint a mural on an outside wall. • This figure is a scale drawing of the wall. The width is 28 inches and the length is 11 inches. What is the area of the actual wall? • Step 1: Find the number of feet represented by 1 inch in the drawing. • = 1in in this drawing equals 1.5ft on the actual wall • Step 2: Find the height of the actual wall labeled 11in in the drawing. • = The height of the actual wall labeled 11in is 16.5ft • Step 3: Find the length of the actual wall labeled 28in in the drawing • = The length of the actual wall is 42ft • Step 4: Since the area is length times width, the area of the actual wall is • 16.5ft × 42ft = 693 ft²

  7. Example 2 – Try It • The farmers one field. The picture shows 3 inches represents • 1 acre. The width is 11inches and the length is 16inches. What is the area of the actual field. • Step 1- Figure out what the scale of the drawing is. • Step 2 – Calculate all of the numbers between the scale drawing and the actual size. • Width = 33 acres Length = 48 acres • Step 3 – Find the area of the actual object. • 33 × 48 = 1584 acres

  8. Example 1 continued • Reflect: • How could you solve the example without having to determine the number of feet represented by 1 inch? • Cross Multiply • = • Your Turn pg 239 # 5-6

  9. Explore Activity 2 page 239 • Do on your own • Check with a partner • Go over as a class

  10. Assignments & assessments • Independent Practice pg 241 # 6 – 11 on your own • Guided Practice pg 240 # 1 – 5 on your own

  11. SKIP THIS SECTOIN8.2 Geometric drawings How can you draw shapes that satisfy given conditions?

  12. Notes – Do all of this in your notebook • Explore Activity 1 & 2 pg 243-244 – as a class • Guided Practice pg 245 1-4 try on your own – go over as a class

  13. Assignments & Assessments

  14. SKIP THIS SECTOIN 8.3 Cross sections How can you identify cross sections of three-dimensional figures?

  15. Notes – Do all of this in your notebook • Explore Activity 1 & 2 pg247 - 248 – as a class • Guided Practice pg249 1-4 try on your own – go over as a class

  16. Assignments & assessments

  17. 8.4 angle relationships How can you use angle relationships to solve problems?

  18. Measuring Angles • Explore activity pg 251 • Complete as a class in your notes.

  19. Angle Pairs & one step equations • Use the diagram on pg 252 – draw it in your notes • Step 1: Name the pair of vertical angles • Angles that are opposite angles formed by intersecting lines • ∠AFB & ∠DFE • Step 2: Name the pair of adjacent angles • Angles that share vertex and a side but do not overlap • ∠AFB & ∠BFD • Step 3: Name the pair of supplementary angles • Angles formed by intersecting lines are supplementary • ∠AFB & ∠BFD

  20. Angle Pairs & one step equations – Cont. • Step 4: Name the two pairs of supplementary angels that include ∠ DFE • Any angle that forms a line with ∠DFE • Step 5: Find the measure of ∠ AFB • Use the fact that ∠AFB & ∠BFD in the diagram are supplementary angles to find m∠AFB. • m∠AFB + m∠BFD = 180° x + 140° = 180° x + 140° - 140° = 180° - 140° x = 40° the measure of ∠AFB Your turn on page 253 #5-9 with the person sitting next to you.

  21. Angle pairs & two – step equations • Draw the picture from Example 2 page 254 • Step 1: Identify their relationship between ∠EHF and ∠FHG • Since angles ∠EHF and ∠FHG form a straight line the sum of the measures of the angles are 180°. • ∠EHF and ∠FHG are supplementary angles • Step 2: Write and solve an equation to find x • m∠EHF + ∠FHG = 180° 2x + 48° = 180° 2x + 48° - 48° = 180° - 48° 2x = 132° 2x/2 = 132°/2 X = 66°

  22. Angle pairs & two – step equations • Step 3: Find the measure of ∠EHF • Substitute 66° for x and multiply • m∠EHF = 2x = 2(66°) = 132° • Check • Confirm that ∠EHF and ∠FHG are supplementary. • m∠EHF + ∠FHG = 180° 132° + 48° = 180° 180° = 180°

  23. Your turn • Look example B on page 255 – on your own and discuss as a class • Your turn page 255 #10-11

  24. Assignments & Assessments

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