The document describes an activity investigating the relationship between the sides of a right triangle using grid paper. Students are given three right triangles formed by squares and asked to find the area of each square. They discover that the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides, relating to the Pythagorean theorem.

1. WHAT is the relationship
among the sides of a right
triangle?
Course 3, Inquiry Lab before Lesson 5-5
Geometry

2. • 8.G.6
Explain a proof of the Pythagorean Theorem and its converse.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 3, Inquiry Lab before Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Geometry

3. Course 3, Inquiry Lab before Lesson 5-5
Activity
continued

Geometry
Three square tents at the school carnival are situated as shown
below. The backs of the orange tent and the green tent form a
right angle. The back of the blue tent finishes the triangle.
Using grid paper can help to investigate the relationship among
the sides of a right triangle.
In each figure below, the sides of three squares form a right
triangle.

4. Course 3, Inquiry Lab before Lesson 5-5
Geometry
Find the area of each square that is
attached to the triangle. Record your
results in the table below. The first one is
already done for you. Use the figures at
the right to help find the area of partial
grids.
What relationship exists among the areas of the three squares
bordering each triangle?_____________________________________
________________________________________________________

5. Course 3, Inquiry Lab before Lesson 5-5
WHAT is the relationship
among the sides of a right
triangle?
Geometry