Pythogaras' theorum Flashcards
What is the Pythagorean theorem formula?
a² + b² = c²
In a right triangle, what does ‘c’ represent in the Pythagorean theorem?
The length of the hypotenuse.
True or False: The Pythagorean theorem applies to all triangles.
False
What type of triangle does the Pythagorean theorem apply to?
Right 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 lengths of the two legs are 5 and 12. The length of the hypotenuse is ____.
13
What do you call a triangle with one angle measuring 90 degrees?
A right triangle.
If a right triangle has a hypotenuse of 10 units and one leg of 6 units, what is the length of the other leg?
8 units.
True or False: The Pythagorean theorem can be used to determine if a triangle is a right triangle.
True
What is the relationship between the sides of a 30-60-90 triangle?
The sides are in the ratio 1 : √3 : 2.
If the hypotenuse is 15 units and one leg is 9 units, how would you find the length of the other leg?
Use the formula: other leg = √(15² - 9²).
What is the Pythagorean theorem used for in real life?
To calculate distances, heights, and in construction.
In the equation a² + b² = c², what do ‘a’ and ‘b’ represent?
The lengths of the two legs of the right triangle.
If a right triangle has legs of lengths 7 and 24, what is the hypotenuse?
25 units.
Which of the following is a correct application of the Pythagorean theorem? a) Finding the area of a triangle b) Finding the length of a diagonal in a rectangle c) Calculating the perimeter of a triangle.
b) Finding the length of a diagonal in a rectangle.
Fill in the blank: The Pythagorean theorem is named after the Greek mathematician ____.
Pythagoras.
What is the converse of the Pythagorean theorem?
If a² + b² = c², then the triangle is a right triangle.
True or False: The Pythagorean theorem can only be used with integer values.
False
If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?
Yes, it satisfies the Pythagorean theorem.
What is the Pythagorean triple for the sides of a 3-4-5 triangle?
3, 4, and 5.
If the lengths of the legs of a right triangle are both equal, what type of triangle is it?
An isosceles right triangle.
Complete the statement: The sum of the squares of the legs equals the square of the ____.
hypotenuse.
If a right triangle has a hypotenuse of 20 units and one leg of 15 units, what is the length of the other leg?
√(20² - 15²) = 5√3 units.
What is the area of a right triangle with legs measuring 6 and 8 units?
24 square units.
