What is the distance between two points in a coordinate plane?

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

If Jane walks 6 blocks east and Miguel walks 8 blocks north, how do you find the distance between their schools?

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

What is the simplest radical form of a number?

The simplest radical form of a number is when the radical is simplified as much as possible, meaning no perfect square factors remain under the radical.

How do you simplify $$\text{sqrt}(30)$$ ?

$$\text{sqrt}(30)$$ is already in simplest form because 30 has no perfect square factors.

What is the value of $$x$$ in the equation $$x^2 + 6^2 = 10^2$$ ?

To find $$x$$ , rearrange the equation: $$x^2 = 10^2 - 6^2 = 100 - 36 = 64$$ , so $$x = \text{sqrt}(64) = 8$$ .

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

In a right triangle, the length of the hypotenuse is always greater than either of the other two sides.

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

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

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

To verify if a triangle with sides a, b, and c is a right triangle, check if $$a^2 + b^2 = c^2$$ holds true, where c is the longest side.

8. 1 Pythagorean Theorem & Its Converse Flashcards

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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 a Pythagorean Triple?

Back

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

How can you determine if a set of numbers is a Pythagorean Triple?

Back

Tags

CCSS.8.G.B.8

4.

FLASHCARD QUESTION

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

5.

FLASHCARD QUESTION

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Tags

CCSS.8.G.B.8

6.

FLASHCARD QUESTION

Front

What is the length of the hypotenuse if the other two sides are 6 in. and 8 in.?

Back

Tags

CCSS.8.G.B.7

7.

FLASHCARD QUESTION

Front

How do you find the length of a missing side in a right triangle?

Back

Tags

CCSS.8.G.B.7

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