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Telescoping triangles

Telescoping triangles. Illinois State Standards 7.7.01 Select 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.

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Telescoping triangles

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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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