Pythagoras Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right-angled 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 a right-angled triangle?

Back

A right-angled triangle is a triangle in which one of the angles is exactly 90 degrees.

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

Given the sides 6, 8, and 10, which can represent a right triangle?

Back

Yes, these sides can represent a right triangle because 6² + 8² = 10² (36 + 64 = 100).

Front

If a triangle has sides 6, 6.7, and 3, which is the hypotenuse?

Back

The hypotenuse is 6.7, as it is the longest side.

Front

What type of triangles can the Pythagorean theorem be applied to?

Back

The Pythagorean theorem can only be applied to right triangles.

Front

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

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

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

If the lengths of two sides of a right triangle are 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the sides satisfy the Pythagorean theorem: 3² + 4² = 5² (9 + 16 = 25).