Pythagorean Theorem Review

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 is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Tags

CCSS.8.EE.A.2

Front

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

Back

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

Tags

CCSS.8.G.B.7

Front

What is the formula to find the length of a missing side in a right triangle?

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Tags

CCSS.8.G.B.8

Front

If the lengths of the two legs of a right triangle are 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, so c = √169 = 13.

Tags

CCSS.8.G.B.7

Front

What is the first step in solving for c in the equation a² + b² = c²?

Back

The first step is to substitute the known values of a and b into the equation.

Tags

CCSS.8.G.B.8

Front

If a right triangle has a hypotenuse of 10 and one leg of 6, how do you find the length of the other leg?

Back

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

Tags

CCSS.8.G.B.7

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8