Virginia SOL 8.MG.4.b
The Standard
Determine whether a triangle is a right triangle given the measures of its three sides.
Virginia Standards of Learning for Mathematics · The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the longest side and treat it as the possible hypotenuse. They square all three lengths and check whether the two smaller squares sum to the largest square.
What Mastery Looks Like
- Students identify the longest side as the possible hypotenuse. They correctly test the side lengths using a² + b² = c² and support their conclusion with an equation.
Common Misconceptions
- Students may use the two shortest sides as the hypotenuse or compare side lengths without squaring them. Some assume any triangle with three whole-number sides is a right triangle.
How to Assess It
- Give students side lengths 8, 15, and 17. Ask them to show a calculation, name the hypotenuse, and justify their conclusion.
Lesson moves
Ways to Teach It
Build triangles with straws cut to given lengths, then measure one angle and compare the result with the Pythagorean test.
Ask students to explain why the longest side must be used for c when testing side lengths 9, 12, and 15.
Play a card sort matching side-length sets with completed calculations and labels of right triangle or not right triangle.
Test whether a wheelchair ramp, wall height, and ground distance form a right triangle using a labeled scale drawing.
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Printable 8.MG.4.b Worksheet
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Related Standards
- 5.MG.2.a
Investigate and develop a formula for determining the area of a right triangle.
- 5.MG.3.c
Identify congruent sides and right angles using geometric markings to denote properties of triangles.
- 8.MG.4.d
Determine the measure of a side of a right triangle, given the measures of the other two sides.
- 8.MG.4.c
Identify the parts of a right triangle (the hypotenuse and the legs) given figures in various orientations.
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