Pythagorean Theorem Exit Ticket

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 the hypotenuse in a right triangle?

Back

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

Front

If a = 12 and b = 35, how do you find c using the Pythagorean Theorem?

Back

To find c, use the formula c² = a² + b². Substitute the values: c² = 12² + 35² = 144 + 1225 = 1369. Then, take the square root: c = √1369 = 37.

Tags

CCSS.8.G.B.8

Front

Which set of side lengths forms a right triangle?

Back

A set of side lengths forms a right triangle if they satisfy the Pythagorean Theorem. For example, the lengths 9, 40, and 41 satisfy the theorem since 9² + 40² = 41².

Tags

CCSS.8.G.B.8

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: if c is the hypotenuse, then a = √(c² - b²) or b = √(c² - a²).

Tags

CCSS.8.G.B.7

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

How can you verify if a triangle is a right triangle using side lengths?

Back

To verify if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

What is the value of c if a = 24 and b = 70?

Back

Using the Pythagorean Theorem: c² = 24² + 70² = 576 + 4900 = 5476. Therefore, c = √5476 = 74.

Tags

CCSS.8.G.B.7

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles. For non-right triangles, other methods such as the Law of Cosines are used.

Tags

CCSS.8.G.B.8