Virginia SOL 8.MG.4.d
The Standard
Determine the measure of a side of a right triangle, given the measures of the other two 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 identify the legs and hypotenuse of a right triangle. They substitute two known lengths into the Pythagorean equation and solve for the missing length.
What Mastery Looks Like
- Students identify the hypotenuse before choosing an equation. They find a missing leg or hypotenuse, give an exact or rounded value as requested, and check that the length is reasonable.
Common Misconceptions
- Students may treat the unknown side as the hypotenuse even when it is a leg. They may add or subtract squared values correctly but forget to take the square root.
How to Assess It
- Exit ticket: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the other leg and show each step.
Lesson moves
Ways to Teach It
Give students labeled right triangle cutouts to measure, calculate the missing side, and compare the calculated length with the measured length.
Ask students to explain why finding a missing leg requires subtraction, while finding the hypotenuse requires addition.
Play a matching game with cards showing right triangles, equations, squared values, and missing side lengths.
Present a ladder against a wall with two known measurements, then have students calculate the missing height or ladder length.
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Related Standards
- 5.MG.2.a
Investigate and develop a formula for determining the area of a right triangle.
- 7.MG.2.g
Given angle measures in a quadrilateral or triangle, determine unknown angle measures in a similar quadrilateral or triangle.
- 7.MG.2.f
Solve a proportion to determine a missing side length of similar quadrilaterals or triangles.
- 8.MG.4.b
Determine whether a triangle is a right triangle given the measures of its three sides.
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