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← The Baudhayana-Pythagoras Theorem

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Lesson 7 of 16

Testing a triangle without a protractor

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6 min

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You measure a gate's three bars: 60, 80 and 100 cm. You have no protractor, a tool for measuring angles. Is the corner between the 60 and 80 bars exactly 90°?

Three lengths: 60, 80 and 100. Do the two shorter add to more than the longest? Yes.
Step 1 of 4
  1. Three lengths: 60, 80 and 100. Do the two shorter add to more than the longest? Yes.
  2. Square the two shorter and add: 3600 + 6400 = 10000.
  3. Square the longest too: 10000. Equal — the corner is exactly 90°.
  4. A near miss: 8, 9, 12 gives 145, but 12 × 12 is 144. Not a right angle.

Yes. The corner between the 60 and 80 bars is exactly 90°.

Rule: Two checks, in order. First, do the two shorter lengths add to more than the longest? If not, there is no triangle. Then square the two shorter and compare with the longest squared. Equal totals happen only at a square corner. So equal means the two shorter sides meet at exactly 90°.

Slide the third bar. Find where the corner is exactly 90°.

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