6.3 Similar Figures and Scale Drawings


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Chapter 6, Section 3: Similar Figures and Scale Drawings

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6.3 Similar Figures and Scale Drawings

  1. 1. Chapter 6, Section 3: Similar Figures and Scale Drawings Ratios Make Things Similar!
  2. 2. Similar Figures <ul><li>Figures that are SIMILAR have the SAME SHAPE, but NOT necessarily the same SIZE. </li></ul><ul><li>Similar Figures have the Same Angles and Sides they are called Corresponding Angles and Corresponding Sides . </li></ul><ul><li>Corresponding = The Same </li></ul>
  3. 3. These Figures Are Similar The symbol ~ means “ is similar to ”. To the right, ΔABC ~ ΔXYZ.
  4. 4. Similar Figures Have Two Properties. <ul><li>The Corresponding angles have equal measures. </li></ul><ul><li>The lengths of the corresponding sides are in proportion. </li></ul>
  5. 5. Example Problems <ul><li>Parallelogram ABCD ~ parallelogram EFGH. Find the value of X . </li></ul><ul><li>Hint: Write a proportion for corresponding sides. </li></ul>Side AB corresponds to side EF. So x/18 = 16/24 Write the CROSS PRODUCT. Divide and Simplify to SOLVE for X . X = 12
  6. 6. Try This… <ul><li>Parallelogram KLMN is similar to parallelogram ABCD in the previous example. Find the value of Y . </li></ul><ul><li>Remember, X = 12 on Parallelogram ABCD. </li></ul>
  7. 7. Indirect Measurements <ul><li>Similar Figures can be used to measure things that are difficult to measure otherwise. </li></ul><ul><li>Compare something you know the measurements of to something you don’t know the measurements of. </li></ul><ul><li>PROPORTIONS! </li></ul>
  8. 8. Indirect Measurements <ul><li>A tree casts a shadow of 10feet long. A 5foot woman casts a shadow of 4feet. The triangle shown for the woman and her shadow is similar to the triangle shown for the tree and its shadow. How tall is the tree? </li></ul>The Tree Is12.5 Feet Tall
  9. 9. REMEMBER TO KEEP YOUR RATIOS INLINE!!! THIS compared to THAT. THIS AND THAT have to be in the same ORDER every TIME .
  10. 10. Try This One and Draw It Yourself <ul><li>A building is 70 feet high and casts a 150 foot shadow. A nearby flagpole casts a 60 foot shadow. Draw a picture/diagram of the building, the building’s shadow, the flagpole, and it’s shadow. Use the triangles created to find the height of the flagpole. </li></ul>The Flagpole is 28 feet tall.
  11. 11. Things That Are Scaled… <ul><li>Model Trains </li></ul><ul><li>(Scale Models of Real Trains, Just Tinier!) </li></ul><ul><li>Model Cars </li></ul><ul><li>(Again, Scale Models of the Real Thing) </li></ul><ul><li>Maps </li></ul><ul><li>(Scale Drawings of the Earth) </li></ul><ul><li>Blue Prints (Which Are No Longer Blue) </li></ul><ul><li>(Scale Drawing of a Building) </li></ul>
  12. 12. Scale Drawings <ul><li>Scale Drawings are enlarged or reduced drawings that are SIMILAR to an ACTUAL object or place. </li></ul><ul><li>The RATIO of a distance in the drawing (or representation) to the corresponding actual distance is the SCALE of the drawing. </li></ul>
  13. 13. Guess Where This Is… This is the ratio for this Scale Representation!
  14. 14. Try This One… <ul><li>The scale of the map is 1 inch : 40 miles. About how far from Atlanta is Athens, if the map distance is 1.5 inches? </li></ul><ul><li>Write a proportion. </li></ul><ul><li>Write Cross Products. </li></ul><ul><li>Simplify. </li></ul><ul><li>Athens is about 60 miles from Atlanta. </li></ul>
  15. 15. Assignment #44 <ul><li>Page 291-292: 5-18 all, 20-22 all. </li></ul><ul><li>REMEMBER TO WRITE ALL OF YOUR UNITS! </li></ul><ul><li>If you’re dealing with Gallons for Minute, write Gallon per Minute! </li></ul>