What is the value of c if a = 5 and b = 12?

Using the Pythagorean Theorem: $$c = \text{sqrt}(5^2 + 12^2) = \text{sqrt}(25 + 144) = \text{sqrt}(169) = 13$$ .

What is the first step to solve for a missing side in a right triangle?

Identify which sides are known (legs or hypotenuse) and apply the Pythagorean Theorem accordingly.

If c = 10 and a = 6, how do you find b?

Rearranging the Pythagorean Theorem: $$b = \text{sqrt}(c^2 - a^2) = \text{sqrt}(10^2 - 6^2) = \text{sqrt}(100 - 36) = \text{sqrt}(64) = 8$$ .

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 a common misconception about the Pythagorean Theorem?

A common misconception is that it can be used for all triangles, but it only applies to right triangles.

How can you verify if a triangle is a right triangle using the Pythagorean Theorem?

To verify, check if the lengths of the sides satisfy the equation $$a^2 + b^2 = c^2$$ .

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

In a 3-4-5 triangle, the sides satisfy the Pythagorean Theorem: $$3^2 + 4^2 = 5^2$$ , confirming it is a right triangle.

What is the formula for finding the area of a right triangle?

The area of a right triangle is given by: $$\text{Area} = \frac{1}{2} \times a \times b$$ , where a and b are the lengths of the legs.

Pythagorean Theorem Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

How do you find the length of a leg in a right triangle?

Back

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

If a = 3 and b = 4, what is the length of the hypotenuse?

Back

5.

FLASHCARD QUESTION

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem, it is not a right triangle.

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

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