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# Pythagorean & Triangle Inequality Theorems Card Sort

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This card sort activity requires students to use the Triangle Inequality Theorem, Converse of the Pythagorean Theorem, and Pythagorean Inequality Theorems to classify triangles as Acute, Obtuse, Right, or Not a Triangle when given 3 side lengths.

Students will cut out the 20 boxes and then use the 3 theorems to determine which type of triangle the 3 side lengths represent. Students will then glue that triangle under the corresponding category on the answer sheet.

The answer sheet is divided into 4 categories: Acute, Obtuse, Right, and Not a Triangle. Next to each category is a QR code that links to the theorem that pertains to each type of triangle.
• QR Code readers can be found for free in both the Apple & Android app store.
• QR codes do not require data or internet access for students to use them.

The following 3 Theorems are used in this activity:
• Triangle Inequality Theorem
- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
• Converse of the Pythagorean Theorem
- If the sum of the squares of the lengths of the shortest sides of a triangle is equal to the square of the length of the longest side, then the triangle is a right triangle.
• Pythagorean Inequality Theorem
- If the square of the length of the longest side of a triangle is greater than the sum of the two squares of the lengths of the other two sides, the triangle is obtuse.
- If the square of the length of the longest side of a triangle is less than the sum of the two squares of the lengths of the other two sides, the triangle is acute.

Please view the preview for an exact view of the completed activity.

This product is also part of the following money saving bundles
Right Triangles & Trigonometry Activity Bundle
High School Geometry Bundle - All My Geometry Products for 1 Low Price

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Teaching Duration
45 minutes
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