Florida B.E.S.T. MA.8.GR.1.3
The Standard
Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students order three side lengths and compare the sum of the two shorter lengths with the longest. For valid triangles, they compare squared lengths to decide whether the triangle is right.
What Mastery Looks Like
- Students correctly identify the longest side and show the needed comparisons. They can decide whether three lengths form a triangle and whether that triangle is right.
Common Misconceptions
- Students may compare the wrong sides instead of using the longest side. Some think two shorter sides may equal the longest side. Others forget to square the lengths when checking for a right triangle.
How to Assess It
- Exit ticket: Classify 6, 8, 10; 4, 5, 10; and 5, 6, 7 as impossible, right, or non-right. Show each comparison.
Lesson moves
Ways to Teach It
Cut straws to given lengths, join their ends, and record which sets close to make a triangle.
Ask students to explain why lengths 3, 4, and 7 do not make a triangle, even though the shorter sides reach the longest.
Give teams cards with side-length triples to sort into impossible, right, and non-right groups, then check another team's work.
Use measurements from a ladder, wall, and floor to decide whether the setup creates a right triangle.
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Related Standards
- MA.912.GR.1.3
Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
- MA.8.GR.1.1
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
- MA.912.T.1.4
Solve mathematical problems involving finding the area of a triangle given two sides and the included angle.
- MA.912.GR.1.2
Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
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