Understanding and Applying the Pythagorean Theorem

Introduction to the Pythagorean Theorem00:00

The video introduces the Pythagorean theorem, explaining the formula C² = A² + B², where C is the hypotenuse of a right triangle and A and B are the other two sides.

Example 1: Calculating the Hypotenuse01:00

An example is given with a right triangle where sides A and B are 5 and 12. The hypotenuse C is calculated to be 13 using the theorem.

Example 2: Solving for a Triangle's Side02:14

The video shows how to solve for a side of a triangle when the hypotenuse is known, demonstrating simplification of radicals in the process.

Example 3: Calculating the Area of a Square with a Diagonal03:30

A problem is presented involving a square with a diagonal length of 12 inches, using the theorem to find the side's length and calculate the area.

Example 4: Finding the Perimeter of a Rhombus06:06

The video solves for the perimeter of a rhombus using its diagonals, applying the theorem to find the length of its sides.

Example 5: Calculating Area of an Isosceles Trapezoid08:30

The area of an isosceles trapezoid is calculated by finding the height using the Pythagorean theorem and then applying the area formula for trapezoids.