How do you calculate the distance between the points (5, 0) and (3, -2)?

Using the Distance Formula: $$d = \text{sqrt}((5 - 3)^2 + (0 - (-2))^2) = \text{sqrt}(2^2 + 2^2) = \text{sqrt}(4 + 4) = \text{sqrt}(8) = 2\text{sqrt}(2)$$ .

What is the significance of the hypotenuse in a right triangle?

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

What is the distance between the points (2, 3) and (5, 7)?

Using the Distance Formula: $$d = \text{sqrt}((5 - 2)^2 + (7 - 3)^2) = \text{sqrt}(3^2 + 4^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

What does it mean if two sides of a triangle are equal?

If two sides of a triangle are equal, the triangle is isosceles, and the angles opposite those sides are also equal.

How can you verify if a triangle is a right triangle using the lengths of its sides?

To verify if a triangle is a right triangle, check if the lengths satisfy the Pythagorean Theorem: $$a^2 + b^2 = c^2$$ .

What is the distance between the points (4, 2) and (3, 4)?

Using the Distance Formula: $$d = \text{sqrt}((4 - 3)^2 + (2 - 4)^2) = \text{sqrt}(1^2 + (-2)^2) = \text{sqrt}(1 + 4) = \text{sqrt}(5)$$ .

What is the formula for the area of a square?

The area of a square is calculated as: $$\text{Area} = \text{side}^2$$ .

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

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, as stated in the Pythagorean Theorem.

Distance Formula and Pythagorean Theorem Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Distance Formula?

Back

Tags

CCSS.HSG.GPE.B.7

2.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

How do you find the hypotenuse of a right triangle?

Back

Tags

CCSS.8.G.B.8

4.

FLASHCARD QUESTION

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to reduce it to its simplest form, making it easier to understand or work with.

5.

FLASHCARD QUESTION

Front

If a triangle has sides of length 3 and 4, what is the length of the hypotenuse?

Back

Tags

CCSS.8.G.B.8

6.

FLASHCARD QUESTION

Front

What is the formula for finding the distance between two points (x1, y1) and (x2, y2)?

Back

Tags

CCSS.HSG.GPE.B.7

7.

FLASHCARD QUESTION

Front

What is the relationship between the areas of squares in the Pythagorean Theorem?

Back

The sum of the areas of the two smaller squares (a^2 and b^2) is equal to the area of the larger square (c^2).

Tags

CCSS.8.G.B.8

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