Section 1
Triangle Inequality Theorem
Property
For any triangle with side lengths , , and , the sum of any two sides must be greater than the third side:
In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to draw and analyze triangles using side lengths and angle measures, including the Triangle Inequality Theorem — the rule that the sum of the two shorter sides must be greater than the longest side. Students also explore whether given sets of measurements produce a unique triangle, discovering that three side lengths determine a unique triangle while three angle measures alone do not. The lesson connects these concepts through real-world contexts like constructing borders and creating geometric art designs.
Section 1
Triangle Inequality Theorem
For any triangle with side lengths , , and , the sum of any two sides must be greater than the third side:
Section 2
Range of Possible Lengths for a Third Side
Given two side lengths of a triangle, and , the length of the third side, , must be strictly greater than their positive difference and strictly less than their sum:
Section 3
Non-Unique Triangles: Angle-Angle-Angle (AAA)
When three angle measures are given that sum to , you can draw infinitely many triangles. This is known as the Angle-Angle-Angle (AAA) condition. Because no side lengths are specified, the triangles will have the exact same shape but can be drawn in many different sizes. Therefore, the AAA condition does not produce a unique triangle.
Section 4
Summary: Conditions for Unique, Multiple, or No Triangles
When given three side lengths or three angle measures, you can determine how many triangles can be drawn:
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Section 1
Triangle Inequality Theorem
For any triangle with side lengths , , and , the sum of any two sides must be greater than the third side:
Section 2
Range of Possible Lengths for a Third Side
Given two side lengths of a triangle, and , the length of the third side, , must be strictly greater than their positive difference and strictly less than their sum:
Section 3
Non-Unique Triangles: Angle-Angle-Angle (AAA)
When three angle measures are given that sum to , you can draw infinitely many triangles. This is known as the Angle-Angle-Angle (AAA) condition. Because no side lengths are specified, the triangles will have the exact same shape but can be drawn in many different sizes. Therefore, the AAA condition does not produce a unique triangle.
Section 4
Summary: Conditions for Unique, Multiple, or No Triangles
When given three side lengths or three angle measures, you can determine how many triangles can be drawn:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter