Lesson Plan

The Distance Formula and the Pythagorean Theorem


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Big Ideas




This lesson covers the distance formula and the Pythagorean theorem, their uses, and their similarities. By the end of this lesson, students will be able to:

  • find the shortest distance between two points on a map.

  • relate the distance formula to the Pythagorean theorem.

Essential Questions

  • What is the relationship between the length of the hypotenuse of a triangle and its legs?

  • What methods do we have to determine the unknown measures of a right triangle?


  • Hypotenuse: In a right triangle, the side opposite the right angle, the longest side of the triangle.

  • Pythagorean Theorem: [IS.1 - All Students] A formula for finding the length of a side of a right triangle when the lengths of the other two sides are given (leg2 + leg2 = hypotenuse2 or  a2 + b2 = c2).  [IS.2 - Struggling Learners]

  • Leg of a Right Triangle: One of the sides of the right triangle other than the hypotenuse. [IS.3 - All Students]


45–60 minutes [IS.4 - All Students]

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