CCSS.Math.Content.8.G.B.7
The Standard
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Common Core State Standards for Mathematics · Geometry
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the legs and hypotenuse of a right triangle, then use squared side lengths to find an unknown length. In three-dimensional figures, they locate or draw right triangles and may solve in two steps.
What Mastery Looks Like
- Students choose the correct sides, write a valid equation, and solve for the missing length. They can find a diagonal inside a rectangular prism and label answers with suitable units.
Common Misconceptions
- Students may treat any side as the hypotenuse instead of finding the side opposite the right angle. They may add side lengths before squaring, forget the square root, or use a face diagonal as a box's space diagonal.
How to Assess It
- Exit ticket: A box measures 6 by 8 by 24 inches. Draw the needed right triangles and find the longest rod that fits inside.
Lesson moves
Ways to Teach It
Make right triangles with rulers and string, measure each side, then compare the measured hypotenuse with the calculated length.
Write a response to: Why must the hypotenuse be isolated before finding a missing leg?
Play a card match game pairing right-triangle diagrams, equations, and missing side lengths.
Calculate the ladder length needed to reach a window when the base must stand a given distance from the wall.
Free download
Printable 8.G.B.7 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.G.B.7, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetBefore This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.G.B.6
Explaining why the theorem works supports choosing and using it to find missing right triangle side lengths.
- CCSS.Math.Content.8.EE.A.2
Finding an unknown side with the Pythagorean Theorem requires solving x² = p and interpreting square roots.
- CCSS.Math.Content.7.NS.A.3
Rational number operations support calculating squares, sums, differences, and side lengths when using the Pythagorean Theorem.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.G.B.8
Finding coordinate distance requires forming a right triangle and using the Pythagorean Theorem to solve for its hypotenuse.
- CCSS.Math.Content.HSG-SRT.C.8
Solving applied right triangles in high school still requires finding missing sides with the Pythagorean Theorem before adding trigonometric ratios.
Keep exploring
Related Standards
- CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other sha...
- CCSS.Math.Content.8.G.B
Understand and apply the Pythagorean Theorem.
- CCSS.Math.Content.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, ...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.