Right Angles and the Pythagorean Theorem

By Susan LoFranco on Apr 24, 2017

This lesson is planned to be done over two days (with an option for three) in either a small group / class or with a Tsingle student.

  • Form right triangle by connecting the origin, a point on the x-axis, and a point on the y-axis
  • Understanding of tracking vertically and horizontally
  • Understand legs vs. hypotenuse on a right triangle, how to solve equations involving  x2
  • Understanding of how to solve square, square root, and factors


pythagorean worksheet clippythagorean answers sheet clipwhat's your angle, pythagoras worksheet clip

pythagorean worksheet clippythagorean answers clip



Vocabulary: Pythagorean Theorem, right angle, hypotenuse, legs, square root, square, factors, prime numbers 

Day 1: 

Pythagorus makes angles out of rope

  • Read "What's Your Angle, Pythagoras?".   Use the following link http://roymath.weebly.com/uploads/1/1/2/7/11275399/6_-_whats_your_angle_pythagoras_booklet.pdf (if a group you can have student break up into smaller groups and read together or you can do as a read aloud)
  • After reading the book student(s) will complete the worksheet "What's Your Angle, Pythagoras?" using media of the student's choice. Discuss with the student their answers to ensure understanding.



Day 2: 

  • After reviewing with the student the Pythagorean Theorem (a2 + b2 = c2) and reviewing the sides or a right triangle (base, perpendicular, hypotenuse, the little box represents a 90 degree angle) explain to the student that you will be working together to solve for the length of the hypotenuse of a right triangle.  Using the "Pythagorean Worksheet" solve problem number one together with the student.  (see answer sheet for solution).  For ease of the lesson the student can use a calculator to figure out the squares and square root of numbers.  If the student is confident have them complete the worksheet using the student's choice of media.  
  • If time permits, the teacher can move on to solving for a third side of the triangle (not the hypotenuse).  It time does not permit this can then be done on Day 3.  Attached are additional worksheets  Pythagorean Worksheet 2 and Answer sheet for solution.  
  pythagorean theorem collage