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![Geometry worksheet in which students develop and apply the Pythagorean Converse to identify right triangles.](https://static.wixstatic.com/media/49609e_cb4bec2fa04c4591a18175d6db0cda5c.jpg/v1/fill/w_404,h_563,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/49609e_cb4bec2fa04c4591a18175d6db0cda5c.jpg)
![Geometry worksheet in which students develop and apply the Pythagorean Converse to classify triangles as acute, right, and obtuse.](https://static.wixstatic.com/media/49609e_5d184fb4d03448398163e5b3e3599df4.jpg/v1/fill/w_404,h_531,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/49609e_5d184fb4d03448398163e5b3e3599df4.jpg)
Activity 3.8
Assignment 3.9
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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.
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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.
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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.
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If a + b < c , then the triangle is an obtuse triangle.