Google Classroom구글 클래스룸
GeoGebra지오지브라 클래스룸
GeoGebra

Understanding Pythagorean Theorem

저자:rborji1, Linda Fahlberg-Stojanovska, John Golden, Lew W. S.
주제:기하

Introduction and Warm‑Up

In this lesson, you’ll explore the Pythagorean Theorem, learn to prove it, and apply it to real‑world and coordinate‑geometry problems.  Before we start, recall what a right triangle is: a triangle with one 90° angle.
Image

Which of these is true about a right triangle?

적용되는 모든 것을 선택하세요.
  • A
  • B
  • C
답안을 점검하세요 (3)

Building a Draggable Right Triangle with Squares

Click and drag the red point. How does it move? Do we always have a right triangle? Why?

Which equation correctly represents the relationship between the sides of a right triangle?

자신의 답을 점검하세요.

Proving the Pythagorean Theorem

  • Let’s prove the theorem by rearranging shapes.  Click on any point and move it and observe how the two smaller squares perfectly fill the largest square.

  • What did you notice during the animation?  Why do the squares’ areas remain the same even when rearranged?

Testing the Converse

If then the triangle must be right‑angled.  Try it!

Common Misconceptions

The Pythagorean Theorem works for all triangles.

적용되는 모든 것을 선택하세요.
  • A
  • B
답안을 점검하세요 (3)

The hypotenuse is always opposite the right angle.

적용되는 모든 것을 선택하세요.
  • A
  • B
답안을 점검하세요 (3)

To find a missing leg, subtract the squared lengths: b² = c² − a².

적용되는 모든 것을 선택하세요.
  • A
  • B
답안을 점검하세요 (3)

Side lengths can be negative.

적용되는 모든 것을 선택하세요.
  • A
  • B
답안을 점검하세요 (3)

Find the missing side

Given a right triangle with legs a = 5 and hypotenuse c = 13, what is the length of the other leg b?

자신의 답을 점검하세요.

Real-Life Problem

Real-Life Problem
A firefighter places a 40‑ft ladder against a wall.  The foot of the ladder is 9 ft from the wall. 

How high up the wall does the ladder reach?

Exit Ticket/ Reflection

  1. “Why does the Pythagorean Theorem apply only to right triangles?”
  2. “Describe one misconception you had and how today’s exploration changed your understanding.”

새 자료

자료 찾기

주제 찾기