TEST: Pythagorean Theorem and Special Right Triangles

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: c² = a² + b².

Front

How do you find the altitude of an equilateral triangle?

Back

To find the altitude (h) of an equilateral triangle with side length (s), use the formula: h = (√3/2) * s. If the perimeter is given, first find the side length by dividing the perimeter by 3.

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. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the 90° angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg. If the leg length is 'a', then the hypotenuse is a√2.

Front

How do you calculate the perimeter of a square?

Back

The perimeter (P) of a square is calculated by the formula: P = 4s, where 's' is the length of one side.

Front

What is the formula for the area of a triangle?

Back

The area (A) of a triangle can be calculated using the formula: A = (1/2) * base * height.

Front

How do you find the length of the diagonal of a square?

Back

The length of the diagonal (d) of a square can be found using the formula: d = s√2, where 's' is the length of a side.

Front

What is the formula for the area of a right triangle?

Back

The area (A) of a right triangle is given by the formula: A = (1/2) * base * height.

Front

How do you find the length of a leg in a right triangle using the Pythagorean Theorem?

Back

To find the length of a leg (a) in a right triangle, rearrange the Pythagorean Theorem: a = √(c² - b²), where 'c' is the hypotenuse and 'b' is the length of the other leg.

Front

What is the significance of the altitude in a triangle?

Back

The altitude of a triangle is the perpendicular segment from a vertex to the line containing the opposite side. It is important for calculating the area of the triangle.