PYTHAGOREAN THEOREM

Pythagorean Theorem

Definition Of Pythagorean Theorem

In a right triangle, if a and b are the measures of the legs and c is the measure of the hypotenuse, then a² + b² = c².

Video Examples: The Pythagorean Theorem

Example of Pythagorean Theorem

The right triangle shown has legs 3 and 4 and hypotenuse 5.

example of Pythagorean Theorem

Solved Example on Pythagorean Theorem

Ques: The radius of the circle is 4 inches. Find the length of side of the square using Pythagorean theorem.

example of Pythagorean Theorem

Choices:

A. 4 inches
B. 8 inches
C. inches
D. inches
Correct Answer: D

Solution:

Step 1: Radius of the circle = 4 inches.
Step 2: Hypotenuse = 2 × 4 = 8 inches.
Step 3: Let s be the side of the triangle. Then s is the base of the right triangle.
Step 4: Pythagorean Theorem states that 'In a right triangle, if a and b are the measures of the legs and c is the measure of the hypotenuse, then a² + b² = c².
Step 5: Using Pythagorean Theorem,we get, example of Pythagorean Theorem

Quick Summary

Applies only to right triangles.
Relates the lengths of the legs to the length of the hypotenuse.
Can be used to find a missing side length if the other two are known.

\[ a^2 + b^2 = c^2 \]

⚠️ Common Mistakes

Applying the theorem to non-right triangles.
Incorrectly identifying the hypotenuse.
Algebra errors when solving for a side.

🌍 Real-World Uses

Construction: Ensuring a building corner is a perfect right angle by using the 3-4-5 triangle.
Navigation: Calculating the shortest distance between two points that are not directly connected due to an obstacle.
Engineering: Calculating the length of a bridge support beam spanning a certain horizontal distance and height.

📋 Standards Alignment

CCSS.MATH.8.G.B.6
CCSS.MATH.8.G.B.7

🍎 Teacher Insights

Use visual aids and real-world examples to illustrate the theorem. Emphasize the importance of correctly identifying the hypotenuse. Provide ample practice problems with varying levels of difficulty.

🎓 Prerequisites

Basic Algebra
Right Triangles
Square Roots

Check Your Knowledge

Q1: In a right triangle, if a = 3 and b = 4, what is c?

5 7 25 9

Q2: If c = 13 and a = 5, what is b?

8 12 144 18

Frequently Asked Questions

Q: What is the hypotenuse?
A: The hypotenuse is the side opposite the right angle in a right triangle. It is also the longest side.

Q: Can the theorem be used to prove if a triangle is right-angled?
A: Yes, if a^2 + b^2 = c^2 holds true for the sides of a triangle, then it is a right triangle.