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

Using the formula: $$b = \text{sqrt}(c^2 - a^2)$$ , we have $$b = \text{sqrt}(10^2 - 6^2) = \text{sqrt}(100 - 36) = \text{sqrt}(64) = 8 cm$$ .

If a right triangle has sides of length 8 cm and 15 cm, what is the length of the hypotenuse?

Using the Pythagorean Theorem: $$c = \text{sqrt}(8^2 + 15^2) = \text{sqrt}(64 + 225) = \text{sqrt}(289) = 17 cm$$ .

What is the converse of the Pythagorean Theorem?

The converse states that if a triangle has sides of lengths a, b, and c, and $$a^2 + b^2 = c^2$$ , then the triangle is a right triangle.

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

You can use the Pythagorean Theorem: If the square of the longest side equals the sum of the squares of the other two sides, then it is a right triangle.

What is the area of a right triangle with base 6 cm and height 8 cm?

The area is given by the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24 cm^2$$ .

If the lengths of the two legs of a right triangle are equal, what type of triangle is it?

It is an isosceles right triangle.

What is the significance of the Pythagorean Theorem in real-world applications?

The Pythagorean Theorem is used in various fields such as architecture, construction, and navigation to calculate distances and ensure structures are built correctly.

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

Find the missing side if one side is 5 cm and the hypotenuse is 13 cm.

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

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

Back

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