Pythagorean Theorem Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What is the formula to find the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Front

Can the lengths 15, 20, and 35 form a right triangle?

Back

No, they cannot form a right triangle because 15² + 20² = 625, while 35² = 1225. The sum of the squares of the two shorter sides does not equal the square of the longest side.

Front

If a TV has a diagonal of 40 inches and a height of 30 inches, how do you find the width?

Back

Use the Pythagorean Theorem: 30² + b² = 40². Solve for b to find the width.

Front

What does it mean if the sum of the areas of two smaller squares equals the area of a larger square?

Back

This is a statement of the Pythagorean Theorem, indicating that the two smaller squares represent the squares of the two legs of a right triangle, and the larger square represents the square of the hypotenuse.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you determine if three lengths can form a triangle?

Back

Use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and physics to calculate distances and angles.

Front

What is an example of using the Pythagorean Theorem in a word problem?

Back

If a ladder is leaning against a wall, with the base of the ladder 3 feet from the wall and the top reaching 4 feet high, you can find the length of the ladder using the theorem: 3² + 4² = c².