Pythagorus Theorem Flashcards
What is the Pythagorean theorem?
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?
Yes, because 3^2 + 4^2 = 5^2.
What is the formula for the Pythagorean theorem?
a² + b² = c², where c is the hypotenuse.
True or False: The Pythagorean theorem only applies to acute triangles.
False.
Fill in the blank: In the triangle with sides a, b, and hypotenuse c, if a = 6 and b = 8, then c = _____
10.
What does the converse of the Pythagorean theorem state?
If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
True or False: The converse of the Pythagorean theorem can be used to prove that a triangle is a right triangle.
True.
What are the conditions for applying the Pythagorean theorem?
The triangle must be a right triangle.
What is the length of the hypotenuse in a triangle with legs of length 7 and 24?
25.
If a triangle has sides measuring 5, 12, and 13, what type of triangle is it?
It is a right triangle.
Fill in the blank: The Pythagorean theorem can be used to find the length of the hypotenuse when two sides are known, but not when _____
only one side is known.
Is it possible for a triangle with sides of lengths 2, 3, and 4 to be a right triangle?
No, because 2^2 + 3^2 is not equal to 4^2.
What is the relationship between the sides of a 30-60-90 triangle?
The lengths of the sides are in the ratio 1:√3:2.
In a right triangle, if one leg measures 9 and the hypotenuse measures 15, what is the length of the other leg?
12.
True or False: The Pythagorean theorem can be used in three-dimensional geometry.
False.
What is the distance formula derived from the Pythagorean theorem?
d = √((x2 - x1)² + (y2 - y1)²).
Fill in the blank: The Pythagorean theorem is named after the Greek mathematician _____
Pythagoras.
What is the value of c in a right triangle if a = 8 and b = 15?
17.
True or False: The Pythagorean theorem can be applied to any polygon.
False.
For the triangle with sides of lengths 6, 8, and 10, is the Pythagorean theorem verified?
Yes, because 6^2 + 8^2 = 10^2.
What is the sum of the squares of the legs in a right triangle with legs of lengths 9 and 12?
225.
What is the hypotenuse of a right triangle if the two legs are equal and each measures x?
x√2.
If a triangle has sides measuring 8, 15, and 17, what can be concluded?
It is a right triangle.
Fill in the blank: The Pythagorean theorem applies to triangles in a _____ plane.
Euclidean.
What is the geometric interpretation of the Pythagorean theorem?
It relates the areas of squares constructed on the sides of a right triangle.
True or False: The Pythagorean theorem can be used for non-right triangles.
False.
