Maryland Math 8.GR.B.5.a

Math8th GradeGeometric Reasoning and Measurement

The Standard

Determine unknown side lengths in right triangles.

Maryland College and Career Ready Standards for Mathematics (2025) · APPLY THE PYTHAGOREAN THEOREM TO REASON ABOUT RIGHT TRIANGLES.

Teacher's field guide

What Students Need to Do: Students find a missing side of a right triangle when two side lengths are given. They identify whether the missing side is a leg or the hypotenuse, then use the Pythagorean theorem.
What Mastery Looks Like: Students add the squares of the legs to find a hypotenuse, or subtract squares to find a leg. They take the square root and give the answer in the correct units.
Common Misconceptions: Students add side lengths instead of their squares. They add squares when finding a leg, or mistake a leg for the hypotenuse. Some forget to take the square root.
How to Assess It: Exit ticket: A right triangle has a 13 cm hypotenuse and a 5 cm leg. Find the other leg and show your calculation.

Lesson moves

Cut 3-by-3, 4-by-4, and 5-by-5 squares from grid paper, then count their unit squares to compare the areas.
Ask: A classmate says a 13-inch hypotenuse and 5-inch leg make an 18-inch missing leg. How would you check that claim?
Match triangle cards labeled 6, 8, ? and 5, ?, 13 to answer cards labeled 10 and 12, then show the calculations.
Sketch a 13-foot ladder with its base 5 feet from a wall, then calculate how high it reaches.

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