Move the sides. See the proof.

SparkClass

A hands-on playground for the most famous relationship in geometry.

CCSS 8.G.B.6
Live Construction
Interactive right triangle with squares on each side Drag the endpoints of the two perpendicular legs to see the three side lengths and square areas update.
01

Build a right triangle. Drag the coral and teal handles—or use the control desk.

a²9
+
b²16
=
c²25

A three-part teaching move

Start with a prediction, make the relationship visible, then let the rearrangement do the explaining.

1

Explore before naming the rule

Ask students to drag the legs and record which square looks largest. Have them predict the area relationship before reading the live equation.

2

Rearrange without adding anything

In proof mode, point out that the outer square and all four triangles stay unchanged. Only their positions move. Compare the leftover area before and after.

3

Break the “whole number” misconception

Try a = 4 and b = 5. Here c = √41, yet c² = 41 exactly. The theorem is about area—even when the hypotenuse is not a whole number.

CCSS 8.G.B.6 alignment: this manipulative supports explaining a proof of the Pythagorean Theorem. The converse requires a separate investigation.