What is the Pythagorean triple?

A Pythagorean triple consists of three positive integers a, b, and c, such that $$a^2 + b^2 = c^2$$ . Example: (3, 4, 5).

What is the value of $$\frac{1}{2}$$ of the hypotenuse if the legs are 6 cm and 8 cm?

First, find the hypotenuse: $$6^2 + 8^2 = c^2$$ , so $$36 + 64 = c^2$$ , thus $$c = 10 cm$$ . Therefore, $$\frac{1}{2}c = 5 cm$$ .

If a right triangle has a hypotenuse of 13 cm and one leg of 5 cm, what is the length of the other leg?

Using the Pythagorean Theorem: $$5^2 + b^2 = 13^2$$ , so $$25 + b^2 = 169$$ , thus $$b = 12 cm$$ .

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.

What is the formula to find the area of a right triangle?

The area of a right triangle is given by $$Area = \frac{1}{2} \times base \times height$$ .

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side.

What is the converse of the Pythagorean Theorem?

The converse 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.

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Yes, because $$8^2 + 15^2 = 17^2$$ (64 + 225 = 289).

Pythagorean Theorem Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

Tags

CCSS.8.G.B.7

2.

FLASHCARD QUESTION

Front

What does the Pythagorean Theorem state?

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).

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.7

4.

FLASHCARD QUESTION

Front

What is the length of the missing side if the hypotenuse is 10 cm and one side is 6 cm?

Back

Tags

CCSS.8.G.B.7

5.

FLASHCARD QUESTION

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The relationship is that the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Tags

CCSS.8.G.B.8

6.

FLASHCARD QUESTION

Front

If the lengths of the two legs of a right triangle are equal, what can be said about the triangle?

Back

Tags

CCSS.HSG.CO.C.10

7.

FLASHCARD QUESTION

Front

How can you find the length of one leg if the hypotenuse is known?

Back

Tags

CCSS.8.G.B.7

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