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

The relationship is that the sum of the squares of the two legs equals the square of the hypotenuse: $$a^2 + b^2 = c^2$$ .

If a right triangle has legs of lengths 8 cm and 15 cm, what is the length of the hypotenuse?

Using the Pythagorean Theorem: $$8^2 + 15^2 = c^2$$ , so $$64 + 225 = c^2$$ , thus $$c = 17$$ .

What is a right triangle?

A right triangle is a triangle that has one angle measuring 90 degrees.

Can the Pythagorean Theorem be used for obtuse or acute triangles?

No, the Pythagorean Theorem only applies to right triangles.

If the lengths of the legs of a right triangle are both equal, what type of triangle is it?

It is an isosceles right triangle.

What is the value of the hypotenuse if both legs of a right triangle are 1 unit?

Using the Pythagorean Theorem: $$1^2 + 1^2 = c^2$$ , so $$1 + 1 = c^2$$ , thus $$c = \text{sqrt}(2)$$ .

If a right triangle has a hypotenuse of 10 units and one leg of 6 units, what is the length of the other leg?

Using the Pythagorean Theorem: $$6^2 + b^2 = 10^2$$ , so $$36 + b^2 = 100$$ , thus $$b = 8$$ .

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

The Pythagorean Theorem is used in various fields such as architecture, construction, and navigation to calculate distances and ensure structures are built correctly.

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

4.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.7

5.

FLASHCARD QUESTION

Front

Find the missing side if one leg is 6 cm and the hypotenuse is 10 cm.

Back

Tags

CCSS.8.G.B.7

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.B.8

7.

FLASHCARD QUESTION

Front

If the hypotenuse is 13 units and one leg is 5 units, what is the length of the other leg?

Back

Tags

CCSS.8.G.B.7

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