Mod 12 - 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 hypotenuse in a right triangle?

Back

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

Front

If one side of a right triangle is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

What does it mean to square a number?

Back

To square a number means to multiply the number by itself. For example, 3 squared (3²) is 3 x 3 = 9.

Front

What is the square root of 16?

Back

The square root of 16 is 4, because 4 x 4 = 16.

Front

In the equation a² + b² = c², what do a and b represent?

Back

In the equation, a and b represent the lengths of the two legs (sides) of a right triangle.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the distance formula in coordinate geometry?

Back

The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.