What is the distance formula derived from the Pythagorean Theorem?

The distance formula between two points (x1, y1) and (x2, y2) is: $$d = \text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

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

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

If a right triangle has legs of lengths 6 and 8, what is the hypotenuse?

Using the Pythagorean Theorem: $$c = \text{sqrt}(6^2 + 8^2) = \text{sqrt}(36 + 64) = \text{sqrt}(100) = 10$$ .

What is the converse of the Pythagorean Theorem?

The converse states that if a triangle has sides of lengths a, b, and c, and $$a^2 + b^2 = c^2$$ , then the triangle is a right triangle.

How do you determine if a triangle is a right triangle using side lengths?

To determine if a triangle with sides a, b, and c is a right triangle, check if $$a^2 + b^2 = c^2$$ holds true.

What is the area of a right triangle?

The area of a right triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

If a ladder is leaning against a wall forming a right triangle, how do you find the height it reaches?

Use the Pythagorean Theorem: If the ladder length is c and the distance from the wall is a, then the height (b) can be found using: $$b = \text{sqrt}(c^2 - a^2)$$ .

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

In a right triangle, the sum of the angles is always 180 degrees, with one angle being 90 degrees and the other two angles being acute.

The Pythagorean Theorem Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.8

2.

FLASHCARD QUESTION

Front

What is the formula to find the hypotenuse in a right triangle?

Back

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.7

4.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.7

5.

FLASHCARD QUESTION

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

6.

FLASHCARD QUESTION

Front

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

Back

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

7.

FLASHCARD QUESTION

Front

If the hypotenuse is 13 and one leg is 5, how do you find the other leg?

Back

Tags

CCSS.8.G.B.7

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