where students teach themselves
A comprehensive geometry curriculum
Geometry for School and Home
Activity 3.8
Assignment 3.9
Previous
Next
Assignment 7.4
The Pythagorean Converse
Objectives
Use the Pythagorean Converse to determine if three numbers are the lengths of the sides of a right triangle.
Use the Pythagorean Converse to classify triangles as acute, right, and obtuse.
About Geometry Worksheet Assignment 7.4:
Assignment 7.4 is an introduction to the converse of Pythagorean Theorem and its application in classifying triangles.
Prerequisite Skills: Apply the Pythagorean Theorem (Assignment 7.2). Classify triangles by types of angles (Assignment 3.13).
Theorems: If the sum of the squares of the lengths of two sides of a triangle equals the square of the length of the third side, then the triangle is
a right triangle.
2 2 2
If a + b = c , then a and b are the lengths of the legs and c is the length of the hypotenuse of a right triangle.
If the sum of the squares of the lengths of the two shorter sides of a triangle is greater than the square of the length of the longest side, then the
triangle is an acute triangle.
2 2 2
If a + b > c , then the triangle is an acute triangle.
If the sum of the squares of the lengths of the two shorter sides of a triangle is less than the square of the length of the longest side, then the triangle is an obtuse triangle.
2 2 2
If a + b < c , then the triangle is an obtuse triangle.