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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 • 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
TRIANGLE INEQUALITY THEOREM The sum of any two side lengths of a triangle is greater than the third side length.
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
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
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
Example 2 – Applying the Triangle Inequality Theorem Tell whether each triangle can have sides with the given lengths. Explain.
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.