Lesson 07: A Proof of the Pythagorean Theorem | Unit 8: Pythagorean Theorem and Irrational Numbers

Multiple Choice

What is the length of the hypotenuse of the right triangle with legs measuring 2 units and 6 units?

• 10
• 8
• 2√10
• √38

Multiple Choice

What is the length of the hypotenuse of the right triangle with legs of 6 units and 8 units?

• 12
• 10
• 14
• 8

Multiple Choice

A line segment is labeled “n” on a square grid. The line segment starts at an intersection point on the grid and slants downward and to the right to an end point that is 1 unit to the right and 3 units down. What is the length of $$n$$ ? (Each small grid square is 1 square unit.)

• √10
• 3
• √5
• 2√2

Multiple Choice

A line segment is labeled “p” on a square grid. The line segment starts at an intersection point on the grid and slants upward and to the right to an end point that is 3 units to the right and 4 units up. What is the value of $$p$$ ? (Each small grid square is 1 square unit.)

• 6
• 7
• 8
• 5

Open Ended

Use the areas of the two identical squares to explain why $$5^2+12^2=13^2$$ without doing any calculations.

Open Ended

What is the exact length of the line segment labeled “l” on the grid? Explain or show your reasoning. (Each grid square represents 1 square unit.)

Open Ended

What is the exact length of the line segment labeled “m” on the grid? Explain or show your reasoning. (Each grid square represents 1 square unit.)

Open Ended

What is the exact length of the line segment labeled “q” on the grid? Explain or show your reasoning. The line segment starts at an intersection point on the grid and slants upward and to the right to an end point that is 4 units to the right and 5 units up. (Each grid square represents 1 square unit.)