Author:
Andrew Amstutz
Subject:
Critical Thinking, Problem-Solving and Communication, Geometry
Material Type:
Lesson Plan
Level:
Middle School, High School
Grade:
9, 10, 11
Tags:
  • Lesson
  • Pythagorean Theorem
  • lesson
  • License:
    Creative Commons Attribution Non-Commercial Share Alike
    Language:
    English
    Media Formats:
    Downloadable docs, Text/HTML

    The Converse of the Pythagorean Theorem

    Overview

    The focus of the lesson is to review and strengthen understanding of the Pythagorean Thm and the Converse of the Pythagorean Thm.  In addition review and strengthen the students algebra skills regarding square roots.

    This cover Ohio Standards in geometry:

    Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

    Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

     

    Review the Pythagorean Theorem

    Create two or three examples on the board, on your own, using the Pythagorean Theorem.  Try to make sure that you find legs and Hypotenuse.  Some good questions to ask are how do we know what the hypotenuse is?  Can we tell with out using the right angle?  Which side should it be if the triangle is right?  Do all triangles fit using the pythagorean theorem?

    Students will be given examples of right triangles with one side missing.  They will then use the pythagorean theorem to solve for the missing side.

    Discovering how to use the converse of the Pythagorean Theorem

    In the worksheet provided there are multiple kinds of triangles, including one set of side that is not a triangle.  Use these to help guide the kids.  When they have all 5 answered check them.  Only tell them how many they have right, but not which ones.  Once they have all 5 correct have them answer the questions on the second page of the activity.  They need to come up with their own generalizations and identify other things they need to pay attention to when dealing with triangles.

    Students will be given a group of 5 sets of 3 sides.  They must determine if the triangle is right, obtuse or acute using any method they like.  After working alone for 10 min, students will be put in groups to compare anwers and come up with a concenus on what kind of triangles exist.

    Classroom Discussion and Wrap Up

    Have all the groups report out on what they came up with.  Have them add the generalizations to their notes and then give them a few more practice problems to try on their own.  This will help show their understanding of the skills learned for the day.

    Students will present their rules to tell what kind of triangles exist given 3 sides.