Pythagoras Theorem

How do you 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.

• Ensure that all three lengths are equal.

• Verify that the sum of the two shorter lengths is greater than the longest length.

• Calculate the area of the triangle formed by the three lengths.

What is an example of a set of lengths that cannot form a right triangle?

• The lengths 2, 3, and 6

• The lengths 3, 4, and 5

• The lengths 5, 12, and 13

• The lengths 6, 8, and 10

What is a right-angled triangle?

• A triangle with all angles less than 90 degrees.

• A triangle in which one of the angles is exactly 90 degrees.

• A triangle with two equal sides and one angle greater than 90 degrees.

• A triangle that has no equal sides.

What is the converse of the Pythagorean theorem?

• If a triangle has side lengths a, b, and c such that a² + b² = c², then the triangle is a right triangle.

• If a triangle is a right triangle, then a² + b² = c².

• If a triangle has side lengths a, b, and c such that a² + b² > c², then the triangle is an acute triangle.

• If a triangle has side lengths a, b, and c such that a² + b² < c², then the triangle is an obtuse triangle.

What is the hypotenuse in a right triangle?

• The shortest side of a right triangle.

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

• The side adjacent to the right angle.

• The side opposite the longest angle.

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

• Acute triangles

• Obtuse triangles

• Right triangles

• Scalene triangles

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

• The sides are in a ratio of 1:2:3

• The sides satisfy the Pythagorean theorem: 3² + 4² = 5² (9 + 16 = 25)

• The sides are equal in length

• The sides form an isosceles triangle

How can you identify the hypotenuse in a triangle labeled with sides x, y, and z?

• The hypotenuse is the side with the greatest length among x, y, and z.

• The hypotenuse is always the shortest side of the triangle.

• The hypotenuse is the side opposite the smallest angle.

• The hypotenuse is the side that is perpendicular to the other two sides.

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

• 3

• 4

• 5

• 6

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

• d = √((x2 - x1)² + (y2 - y1)²)

• d = |x2 - x1| + |y2 - y1|

• d = (x2 - x1) + (y2 - y1)

• d = √((x2 + x1)² + (y2 + y1)²)