Section 1 - Pythagoras Theorem Flashcards
What is the Pythagorean theorem formula?
a² + b² = c²
In the Pythagorean theorem, what does ‘c’ represent?
‘c’ represents the length of the hypotenuse.
True or False: The Pythagorean theorem applies to all triangles.
False, it only applies to right-angled triangles.
If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?
5 units
Fill in the blank: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the _______.
legs
What is the hypotenuse of a right triangle with legs of lengths 6 and 8?
10 units
True or False: The Pythagorean theorem can be used to determine if a triangle is a right triangle.
True
If a² = 49 and b² = 16, what is the value of c?
c = √65
What type of triangle is defined by the Pythagorean theorem?
Right triangle
What is the length of the hypotenuse if one leg is 12 and the other leg is 5?
13 units
What is the relationship between the sides of a 30-60-90 triangle?
The lengths are in the ratio 1:√3:2.
If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?
12 units
What is the distance formula derived from the Pythagorean theorem?
d = √((x₂ - x₁)² + (y₂ - y₁)²)
If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?
Yes, it satisfies the Pythagorean theorem.
In a right triangle, if one leg is doubled, how does that affect the hypotenuse?
The hypotenuse will increase, but the exact length will depend on the original length of the other leg.
What happens if the Pythagorean theorem is not satisfied?
The triangle is not a right triangle.
If both legs of a right triangle are equal, what type of triangle is it?
Isosceles right triangle
What is the square of the hypotenuse if the legs are 9 and 12?
225
Fill in the blank: The Pythagorean theorem can be used to find the _______ of a triangle.
lengths of sides
If a triangle has sides of lengths 8, 15, and 17, what can be said about it?
It is a right triangle.
What is the value of c if a = 9 and b = 12?
c = 15
True or False: The Pythagorean theorem can be used in three-dimensional space.
False, it is specific to two dimensions.
What is the perimeter of a right triangle with legs of 6 and 8?
20 units
What does the term ‘legs’ refer to in the context of the Pythagorean theorem?
The two sides that form the right angle.
If c² = 100, what is the value of c?
10
If a right triangle has legs measuring 5 and 12, what is the area of the triangle?
30 square units
How can you verify that a triangle is a right triangle using the Pythagorean theorem?
Check if a² + b² = c² holds true.
If a right triangle has a hypotenuse of 15 and one leg of 9, what is the length of the other leg?
√186 or approximately 13.64
What is the relationship between the lengths of the sides in a right triangle?
The square of the hypotenuse is equal to the sum of the squares of the other two sides.
