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Exploring Triangle Area Ratios Through Midpoints Construction

This activity involves constructing midpoints on triangle sides to explore segment ratios, area ratios, and similarity of triangles. Learn to measure length and sketch geometric shapes following given specifications in adherence to Illinois State Standards.

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Exploring Triangle Area Ratios Through Midpoints Construction

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  1. Telescoping triangles Illinois State Standards 7.7.01Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles. Sketch, with given specifications, line segments, angles, triangles, and quadrilaterals. 7.7.03 Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0° to 180°) using referents. Connie Stoner & Myra Turner

  2. GIVEN Triangle ∆abc

  3. Construct Midpoints • Construct a midpoint from each side.

  4. Construct midpoint ∆def

  5. Find midpoints of ∆def

  6. Connect midpoints forming ∆ghi

  7. Find midpoints of ∆ghi

  8. Construct ∆jkl using midpoints

  9. SEGMENT rATIOs

  10. Triangle area ratios

  11. observations • Midsegment ratios were all 2:1 • Area ratios were all 4:1 • All triangles similar

  12. Reasoning • Midpoint of each segment ÷ 2, hence • Area of ∆ABC = • Area of ∆DEF = • = • Proving the 4:1 ratio of areas

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