Pythagorean

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Tags

CCSS.8.G.B.8

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Tags

CCSS.4.G.A.2

Front

What is a hypotenuse?

Back

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

Front

If one leg of a right triangle is 3 cm and the other leg is 4 cm, what is the length of the hypotenuse?

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Tags

CCSS.8.G.B.7

Front

Can a triangle with sides 4, 5, and 6 be a right triangle?

Back

No, it cannot be a right triangle because it does not satisfy the Pythagorean Theorem.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) * base * height.

Tags

CCSS.6.G.A.1

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Tags

CCSS.8.G.B.8

Front

If the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

8 cm (Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Tags

CCSS.8.G.B.7

Front

What is the converse of the Pythagorean Theorem?

Back

If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

What is the significance of the Pythagorean Theorem in real life?

Back

It is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Tags

CCSS.8.G.B.8