Exploring Special Right Triangles (45-45-90)

The video tutorial covers the properties of 45-45-90 isosceles right triangles, explaining how they can be formed by cutting a square diagonally. It demonstrates the use of the Pythagorean theorem to find the hypotenuse and identifies a pattern where the hypotenuse is the leg length multiplied by the square root of 2. The tutorial provides examples to illustrate this pattern and addresses common misconceptions. It also explores non-standard cases and concludes with a summary of the key concepts.

What shape is divided to form a 45-45-90 triangle?

• Rectangle

• Circle

• Square

• Triangle

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CCSS.1.G.A.1

CCSS.2.G.A.1

What is the hypotenuse length when both legs are 1 in a 45-45-90 triangle?

• 1

• Square root of 3

• 2

• Square root of 2

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CCSS.8.G.B.8

How do you find the hypotenuse length in a 45-45-90 triangle with leg length 2?

• Square root of 8

• 2 square roots of 2

• 4

• 2

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CCSS.8.G.B.8

What pattern emerges for the hypotenuse in a 45-45-90 triangle?

• Leg length times square root of 2

• Leg length divided by 2

• Leg length plus 1

• Leg length times 2

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CCSS.8.G.B.8

If one leg is 8 in a 45-45-90 triangle, what is the hypotenuse?

• 8

• 8 square roots of 2

• 16

• 4 square roots of 2

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CCSS.8.G.B.8

What is the hypotenuse if one leg is 5 and it's a 45-45-90 triangle?

• 25

• 5 square roots of 2

• 10

• 5

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CCSS.8.G.B.8

How do you solve for a leg length if the hypotenuse is known and doesn't fit the 45-45-90 pattern?

• Multiply hypotenuse by square root of 2

• Divide hypotenuse by square root of 2

• Hypotenuse times 2

• Hypotenuse divided by 2

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CCSS.8.G.B.8

What is the leg length if the hypotenuse is 10 in a 45-45-90 triangle?

• 5

• 10 square roots of 2

• 10

• 5 square roots of 2

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CCSS.8.G.B.8

If the hypotenuse is 5 root 6, what is one possible leg length?

• 5

• 6

• 5 square roots of 3

• 30

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CCSS.8.G.B.8

What is the hypotenuse if the leg length is 4 root 2 in a 45-45-90 triangle?

• 8 root 2

• 4

• 16

• 8

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CCSS.8.G.B.8