What type of triangle is formed if $$c^2 > a^2 + b^2$$ ?

If $$c^2 > a^2 + b^2$$ , the triangle is classified as an obtuse triangle.

Given the sides 7, 24, and 25, classify the triangle.

The triangle is a right triangle because $$25^2 = 7^2 + 24^2$$ (625 = 49 + 576).

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

To find the missing side of a right triangle, use the Pythagorean Theorem: $$c^2 = a^2 + b^2$$ , solving for the unknown side.

If a triangle has sides of lengths 8, 15, and 17, what type of triangle is it?

It is a right triangle because $$17^2 = 8^2 + 15^2$$ (289 = 64 + 225).

What is the relationship between the sides of an acute triangle?

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides: $$c^2

What is the relationship between the sides of an obtuse triangle?

In an obtuse triangle, the square of the longest side is greater than the sum of the squares of the other two sides: $$c^2 > a^2 + b^2$$ .

If the sides of a triangle are 9, 12, and 15, classify the triangle.

The triangle is obtuse because $$15^2 > 9^2 + 12^2$$ (225 > 81 + 144).

How do you find the hypotenuse if the legs of a right triangle are 6 and 8?

Use the Pythagorean Theorem: $$c = \text{sqrt}(6^2 + 8^2) = \text{sqrt}(36 + 64) = \text{sqrt}(100) = 10$$ .

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 Converse Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.8

2.

FLASHCARD QUESTION

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

3.

FLASHCARD QUESTION

Front

How can you determine if three side lengths form a right triangle?

Back

Tags

CCSS.8.G.B.8

4.

FLASHCARD QUESTION

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

5.

FLASHCARD QUESTION

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Tags

CCSS.8.G.B.8

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.G.B.8

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.G.B.8

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