What is the value of $$c$$ if $$a = 6$$ and $$b = 8$$ ?

Using the Pythagorean Theorem: $$c^2 = 6^2 + 8^2 = 36 + 64 = 100$$ , so $$c = 10$$ .

What is the relationship between the sides of a 30-60-90 triangle?

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : $$\sqrt{3}$$ : 2.

What is the relationship between the sides of a 45-45-90 triangle?

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is $$\sqrt{2}$$ times the length of each leg.

How can you estimate the length of a side in a right triangle?

You can use the Pythagorean Theorem to estimate the length of a side by substituting known values and solving for the unknown.

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.

If $$x^2 + 14^2 = 20^2$$ , what is the value of $$x$$ ?

Rearranging gives $$x^2 = 20^2 - 14^2 = 400 - 196 = 204$$ , so $$x = \sqrt{204} \approx 14.4$$ .

What is the distance formula derived from the Pythagorean Theorem?

The distance formula between two points (x1, y1) and (x2, y2) is: $$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$$ .

What is the importance of estimating answers in geometry problems?

Estimating answers helps to quickly check the reasonableness of a solution and can simplify calculations.

How do you find the area of a right triangle?

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

Pythagorean Theorem Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

What is a right triangle?

Back

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

3.

FLASHCARD QUESTION

Front

What is the hypotenuse in a right triangle?

Back

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

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

How do you solve for a missing side when given the hypotenuse and one side?

Back

7.

FLASHCARD QUESTION

Front

Back

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