Topic 4 Pythagoras Theorem Flashcards
(32 cards)
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 only to right-angled triangles.
True
What type of triangle can you apply the Pythagorean Theorem to?
Right-angled triangles.
If one leg of a right triangle is 3 cm and the other leg is 4 cm, what is the length of the hypotenuse?
5 cm
Fill in the blank: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the ______.
other two sides
What is the length of a hypotenuse if the legs are 6 cm and 8 cm?
10 cm
If a² = 49, what is the value of a?
7
What is the first step in using the Pythagorean Theorem?
Identify the lengths of the two legs.
Calculate the length of the hypotenuse if the legs are 5 m and 12 m.
13 m
True or False: The Pythagorean Theorem can be used for any triangle.
False
If c = 13 and a = 5, what is b?
12
What do you do if you know the hypotenuse and one leg, and need to find the other leg?
Use the formula b = √(c² - a²).
Fill in the blank: The Pythagorean Theorem is named after the ancient Greek mathematician ______.
Pythagoras
What is the hypotenuse of a triangle with legs measuring 1 and √3?
2
How do you find the length of a leg if you have the hypotenuse and the other leg?
Use the formula a = √(c² - b²).
If a triangle has sides of length 8, 15, and 17, is it a right triangle?
Yes
What is the relationship between the sides of a right triangle?
The square of the hypotenuse equals the sum of the squares of the other two sides.
Find the value of c if a = 9 and b = 12.
15
If a = 7 and c = 25, what is b?
24
True or False: In a right triangle, the hypotenuse is always the longest side.
True
What can you conclude if a² + b² < c²?
The triangle is obtuse.
What can you conclude if a² + b² > c²?
The triangle is acute.
In a 30-60-90 triangle, if the shorter leg is x, what is the length of the hypotenuse?
2x
