What is the relationship between the sides of a 3-4-5 triangle?

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: $$3^2 + 4^2 = 5^2$$ .

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

Check if the lengths satisfy the Pythagorean Theorem: If a, b, and c are the lengths of the sides, then check if $$a^2 + b^2 = c^2$$ .

What is the distance formula derived from the Pythagorean Theorem?

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

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

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

If a right triangle has legs of lengths 9 and 12, what is the length of the hypotenuse?

Use the Pythagorean Theorem: $$c = \text{sqrt}(9^2 + 12^2) = \text{sqrt}(81 + 144) = \text{sqrt}(225) = 15$$ .

What is the area of a right triangle with a base of 8 feet and a height of 6 feet?

The area A is given by: $$A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 \text{ square feet}$$ .

How do you find the length of a diagonal in a rectangular field?

Use the Pythagorean Theorem: If the lengths of the sides are a and b, then the diagonal d is given by: $$d = \text{sqrt}(a^2 + b^2)$$ .

What is the formula for the perimeter of a right triangle?

The perimeter P of a right triangle is the sum of the lengths of all three sides: $$P = a + b + c$$ .

Applying 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

If one side of a right triangle is 6 feet and the hypotenuse is 10 feet, how do you find the length of the other side?

Back

Tags

CCSS.8.G.B.7

3.

FLASHCARD QUESTION

Front

What is the length of the diagonal of a rectangle with sides 6 feet and 8 feet?

Back

Tags

CCSS.8.G.B.8

4.

FLASHCARD QUESTION

Front

What does 'hypotenuse' mean in a right triangle?

Back

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

5.

FLASHCARD QUESTION

Front

How do you calculate the missing side of a right triangle if you know the lengths of the other two sides?

Back

Tags

CCSS.8.G.B.7

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.8

7.

FLASHCARD QUESTION

Front

If a ladder is leaning against a wall and forms a right triangle with the ground, how do you find the distance from the base of the ladder to the wall?

Back

Tags

CCSS.8.G.B.8

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