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: c² = a² + b².

Tags

CCSS.8.G.B.8

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the side opposite the right angle and is always the longest side of the triangle.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 units.

Tags

CCSS.8.G.B.8

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 shorter sides (legs) equals the square of the longest side (hypotenuse).

Tags

CCSS.8.G.B.8

Front

If the hypotenuse of a right triangle is 10 units and one leg is 6 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = 8 units.

Tags

CCSS.8.G.B.7

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True. The Pythagorean Theorem is applicable only to right triangles.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) can be found using the Pythagorean Theorem: d = √(length² + width²).

Tags

CCSS.8.G.B.7

Front

If a rectangle has a length of 8 inches and a width of 6 inches, what is the length of the diagonal?

Back

Using the formula: d = √(8² + 6²) = √(64 + 36) = √100 = 10 inches.

Tags

CCSS.8.G.B.7

Front

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

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and angles.

Tags

CCSS.8.G.B.8

Front

In a right triangle, if one angle is 30 degrees, what is the relationship between the sides?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the side opposite the 30-degree angle is the shortest.

Tags

CCSS.HSG.CO.C.10