Georgia 8.GSR.8.2
The Standard
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.
Georgia's K-12 Mathematics Standards · Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find missing lengths in right triangles using the Pythagorean Theorem. They locate right triangles inside flat figures and three-dimensional objects, then interpret the answer in context.
What Mastery Looks Like
- Students identify the right triangle, label the hypotenuse, and choose the correct lengths from the context. They solve accurately, including face or space diagonals, and explain what the result means with suitable units.
Common Misconceptions
- Students may treat either leg as the hypotenuse instead of identifying the side opposite the right angle. They may add when finding a missing leg, forget the square root, or use only two dimensions for a space diagonal.
How to Assess It
- Give students this exit ticket: A box measures 3 feet by 4 feet by 12 feet. Find its space diagonal, show the right triangles used, and label the answer with units.
Lesson moves
Ways to Teach It
Build a 3-by-4-by-12 straw prism, then calculate and verify its 13-unit space diagonal with string.
Write a response explaining why the longest side of a right triangle must be the hypotenuse.
Match triangle and prism diagram cards with equation cards, then solve each matched problem for the missing length.
Decide whether a 10-foot ladder reaches an 8-foot window when its base sits 6 feet from the wall.
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Printable 8.GSR.8.2 Worksheet
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Related Standards
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Determine the perimeter of a polygon presented in real-life, mathematical problems.
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- 8.GSR.8.3
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.
- 8.GSR.8
Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.
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