How do you find the area of a 45-45-90 triangle?

For a 45-45-90 triangle with legs of length $$a$$ , the area is $$A = \frac{1}{2} \times a \times a = \frac{a^2}{2}$$ .

What is the diagonal of a square in relation to its side length?

The diagonal $$d$$ of a square with side length $$s$$ is given by the formula $$d = s\text{√}2$$ .

How do you find the side length of a square if the diagonal is known?

To find the side length $$s$$ when the diagonal $$d$$ is known, use the formula $$s = \frac{d}{\text{√}2}$$ .

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse $$c$$ is equal to the sum of the squares of the lengths of the other two sides: $$c^2 = a^2 + b^2$$ .

How can the Pythagorean theorem be applied to special right triangles?

In special right triangles, the Pythagorean theorem can be simplified using known ratios, such as $$c = a\text{√}2$$ for 45-45-90 triangles and $$c = 2x$$ for 30-60-90 triangles.

What is the significance of simplifying radical expressions?

Simplifying radical expressions makes calculations easier and helps in understanding the relationships between numbers, especially in geometry and algebra.

How do you simplify the expression $$\text{√}18$$ ?

To simplify $$\text{√}18$$ , factor it into $$\text{√}(9 \times 2) = 3\text{√}2$$ .

What is the importance of understanding special right triangles in geometry?

Understanding special right triangles is crucial in geometry as they provide shortcuts for calculating side lengths and angles, making problem-solving more efficient.

special right triangles Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a 45-45-90 triangle?

Back

2.

FLASHCARD QUESTION

Front

What is the relationship between the legs and hypotenuse in a 45-45-90 triangle?

Back

3.

FLASHCARD QUESTION

Front

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

Back

4.

FLASHCARD QUESTION

Front

What is a 30-60-90 triangle?

Back

A 30-60-90 triangle is a right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

7.

FLASHCARD QUESTION

Front

What is the formula for the area of a triangle?

Back

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