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

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

What is the Pythagorean Theorem used for?

The Pythagorean Theorem is used to determine the length of a side in a right triangle when the lengths of the other two sides are known.

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

Using the Pythagorean Theorem: $$c^2 = a^2 + b^2$$ , we have $$13^2 = 5^2 + b^2$$ , which simplifies to $$169 = 25 + b^2$$ , so $$b^2 = 144$$ , thus $$b = 12$$ .

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 7, 24, and 25, is it a right triangle?

Yes, because $$25^2 = 7^2 + 24^2$$ (i.e., $$625 = 49 + 576$$ ).

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

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

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

Using the Pythagorean Theorem: $$10^2 = 6^2 + b^2$$ , which simplifies to $$100 = 36 + b^2$$ , so $$b^2 = 64$$ , thus $$b = 8$$ .

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

The area of a right triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

Pythagorean Theorem Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the longest side of a right triangle?

Back

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

2.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem formula?

Back

3.

FLASHCARD QUESTION

Front

If a right triangle has side lengths 6, 8, and 10, which side is the hypotenuse?

Back

The hypotenuse is 10.

4.

FLASHCARD QUESTION

Front

True or False: Side c on a right triangle is ALWAYS the longest.

Back

True.

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

If one leg of a right triangle is 5 and the other leg is 12, what is the length of the hypotenuse?

Back

7.

FLASHCARD QUESTION

Front

What do you call the two shorter sides of a right triangle?

Back

The two shorter sides of a right triangle are called the legs.

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