Maryland Math 8.GR.B.4.b
The Standard
- 8.GR.B.4
- Understand and reason about the Pythagorean Theorem and its extensions.
Use the converse of the Pythagorean Theorem to determine whether a set of three side lengths forms a right triangle, and extend this reasoning to identify whether a triangle is acute or obtuse using Pythagorean inequalities.
Maryland College and Career Ready Standards for Mathematics (2025) · APPLY THE PYTHAGOREAN THEOREM TO REASON ABOUT RIGHT TRIANGLES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students check whether three lengths can form a triangle. They compare the longest side squared with the sum of the other two sides squared. They use the result to decide whether the triangle is right, acute, or obtuse.
What Mastery Looks Like
- They reject 3, 4, 8 because 3 + 4 < 8. They show 6² + 8² = 10² for a right triangle. They classify 5, 5, 6 as acute and 5, 7, 9 as obtuse using squared comparisons.
Common Misconceptions
- Some students compare the lengths without squaring them or forget to square one of the shorter sides. Others call 3, 4, 8 obtuse without checking whether those lengths can form a triangle. Students may also reverse the comparisons for acute and obtuse triangles.
How to Assess It
- Exit ticket: Classify 5, 5, 6; 6, 8, 10; 5, 7, 9; and 3, 4, 8 as acute, right, obtuse, or not a triangle. Show a calculation for each choice.
Lesson moves
Ways to Teach It
Give pairs 5 cm, 7 cm, and 9 cm straws to build a triangle, then compare squared lengths with its measured angle.
Ask, 'Can lengths 3, 4, and 8 make an obtuse triangle?' Have students write a reason before squaring.
Give teams cards marked 5, 5, 6; 6, 8, 10; and 5, 7, 9 to sort and justify using squares.
Show a carpenter's chalk outline with sides 6, 8, and 10 feet; ask students to verify that the corner is square.
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Related Standards
- 5.GR.B.3.a
Classify triangles based on properties (e.g., angle measure, side lengths).
- 8.GR.B.5
Apply the Pythagorean Theorem to solve problems in context.
- 8.GR.B.5.a
Determine unknown side lengths in right triangles.
- 8.GR.A.2
Draw or build triangles using tools (ruler, protractor, technology, or physical manipulatives) given three measures of angles or sides. Determine whether the gi...
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