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Triangle Inequality Activity

Triangle Inequality Activity. Given your piece of spaghetti, break it into three pieces. There are no rules for the size of the pieces, break wherever you want. Try to make a triangle from the three pieces you have. Can it be made? Break into groups – triangles and no triangles

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Triangle Inequality Activity

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  1. Triangle Inequality Activity • Given your piece of spaghetti, break it into three pieces. There are no rules for the size of the pieces, break wherever you want. • Try to make a triangle from the three pieces you have. Can it be made? • Break into groups – triangles and no triangles • Measure sides, and look at relationships between lengths. Summarize

  2. TRIANGLE INEQUALITY THEOREM The sum of any two side lengths of a triangle is greater than the third side length.

  3. Triangle Inequality Activity Extension • Those of you who could make triangles, measure the angles. • How do they relate to the sides of the triangle? • Summarize

  4. Theorems on Angle-Side Relationships in Triangles • If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. IF THEN

  5. Theorems on Angle-Side Relationships in Triangles • If two angles of a triangle are not congruent, then the longer side is opposite the larger angle. IF THEN

  6. Example 1 – Ordering Side Lengths and Angle Measures

  7. Example 2 – Applying the Triangle Inequality Theorem Tell whether each triangle can have sides with the given lengths. Explain.

  8. Example 3 – Finding Side Lengths The lengths of two sides of a triangle are 6 centimeters and 11 centimeters. Find the range of possible lengths of the third side.

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