Geometry: Pythagorean Triples and Triangles
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Questions and Answers

Which set of numbers represents a Pythagorean triple?

  • 4, 5, 6
  • 5, 12, 13 (correct)
  • 6, 8, 10 (correct)
  • 8, 15, 17

Which of the following triples is NOT a commonly known Pythagorean triple?

  • 7, 24, 25
  • 8, 15, 17 (correct)
  • 10, 30, 50
  • 3, 4, 5

If you have a Pythagorean triple of 3, 4, 5, what is the hypotenuse?

  • 6
  • 5 (correct)
  • 4
  • 3

Which of the following sets can be derived by dilating a Pythagorean triple?

<p>10, 30, 50 (D)</p> Signup and view all the answers

Which of these options lists only whole numbers that can form a right triangle?

<p>6, 10, 15 (C), 30, 40, 50 (D)</p> Signup and view all the answers

What is the length of the hypotenuse in a 45°-45°-90° triangle if each leg measures $x$?

<p>$x ext{√}2$ (B)</p> Signup and view all the answers

If the hypotenuse of a 45°-45°-90° triangle is $12 ext{√}2$, what is the length of each leg?

<p>$12$ (A)</p> Signup and view all the answers

In a 45°-45°-90° triangle, if one leg is $8$, what is the length of the other leg?

<p>$8$ (D)</p> Signup and view all the answers

What operation is used to find the hypotenuse from the leg length in a 45°-45°-90° triangle?

<p>Multiply by $√2$ (A)</p> Signup and view all the answers

If the length of each leg in a 45°-45°-90° triangle is $5 ext{√}2$, what is the length of the hypotenuse?

<p>$10$ (B)</p> Signup and view all the answers

What is the hypotenuse if the short leg of a 30°-60°-90° triangle is 5?

<p>10 (B)</p> Signup and view all the answers

If the long leg of a 30°-60°-90° triangle is 12, what is the length of the short leg?

<p>4 adical{3} (A)</p> Signup and view all the answers

What is the formula to find the long leg if the short leg is known?

<p>Multiply the short leg by $ adical{3}$ (C)</p> Signup and view all the answers

Given the hypotenuse of 10, what would the length of the long leg be in a 30°-60°-90° triangle?

<p>10 adical{3}/2 (C)</p> Signup and view all the answers

What is the short leg if the hypotenuse of a 30°-60°-90° triangle is 14?

<p>7 (A)</p> Signup and view all the answers

Flashcards

30°-60°-90° Triangle

A special right triangle with angles measuring 30°, 60°, and 90°.

Short Leg

The side opposite the 30° angle in a 30°-60°-90° triangle.

Long Leg

The side opposite the 60° angle in a 30°-60°-90° triangle.

Hypotenuse

The side opposite the right angle in a 30°-60°-90° triangle.

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30°-60°-90° Triangle Property

The short leg of a 30°-60°-90° triangle is half the length of the hypotenuse.

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Pythagorean Triple

A right triangle where all three side lengths are whole numbers.

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3, 4, 5 Triple

The most common Pythagorean triple, often used in basic geometry problems. It has side lengths of 3, 4, and 5 units.

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5, 12, 13 Triple

A Pythagorean triple with side lengths of 5, 12, and 13 units.

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7, 24, 25 Triple

A Pythagorean triple with side lengths of 7, 24, and 25 units.

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Dilation of Triples

You can create new Pythagorean triples by multiplying all the side lengths of an existing triple by the same whole number.

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45-45-90 Triangle

A right triangle with two congruent legs and two 45-degree angles.

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45-45-90 Ratio

The ratio between the length of a leg and the length of the hypotenuse in a 45-45-90 triangle is 1:√2.

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Finding the Hypotenuse in a 45-45-90 Triangle

To find the hypotenuse of a 45-45-90 triangle, multiply the length of a leg by √2.

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Finding the Leg in a 45-45-90 Triangle

To find the length of a leg in a 45-45-90 triangle, divide the length of the hypotenuse by √2.

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Pythagorean Theorem and 45-45-90 Triangles

The Pythagorean Theorem can be used to verify the lengths of the sides in a 45-45-90 triangle.

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