Pythagorean Theorem

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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the two shorter sides are called the legs, and the longest side opposite the right angle is called the hypotenuse.

Front

Which set of side lengths forms a right triangle? 6, 9, 12; 8, 10, 12; 9, 40, 41; 5, 10, 12

Back

9, 40, 41 forms a right triangle.

Tags

CCSS.8.G.B.8

Front

What type of angle do the legs of a right triangle form?

Back

The legs of a right triangle form a right angle.

Front

Will the following sides make a right triangle? 2.1, 3.5, 2.8

Back

Yes, these sides can form a right triangle.

Tags

CCSS.8.G.B.8

Front

What is the hypotenuse in a right triangle?

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 and the other leg is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; c² = 25; c = 5.

Tags

CCSS.8.G.B.7

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, one angle is exactly 90 degrees, and the sum of the other two angles is 90 degrees.

Tags

CCSS.8.G.A.5

Front

Can a triangle with sides 5, 12, and 13 be a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Tags

CCSS.8.G.B.8

Front

What is an example of a real-world application of the Pythagorean Theorem?

Back

Finding the distance between two points on a coordinate plane or determining the height of a ladder leaning against a wall.

Tags

CCSS.8.G.B.8