What does it mean if $$a^2 + b^2 > c^2$$ ?

If $$a^2 + b^2 > c^2$$ , the triangle is acute, meaning all angles are less than 90 degrees.

What is the area of a right triangle?

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

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 : $$\frac{\text{sqrt}(3)}{2}$$ : 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 $$\text{leg} \times \text{sqrt}(2)$$ .

What is the distance formula derived from the Pythagorean Theorem?

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

What is the converse of the Pythagorean Theorem?

The converse states that if in a triangle, $$a^2 + b^2 = c^2$$ , then the triangle is a right triangle.

How do you determine if a triangle is a right triangle using side lengths?

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

What is the significance of the right angle in a right triangle?

The right angle indicates that the triangle can be analyzed using the Pythagorean Theorem, allowing for the calculation of side lengths and area.

Pythagorean Theorem Flashcards

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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 a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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