Pythagorean Theorem

Description: This quiz tests your understanding of the Pythagorean Theorem, a fundamental concept in geometry that relates the sides of a right triangle.
Number of Questions: 14
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Tags: pythagorean theorem geometry right triangle
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In a right triangle, the side opposite the right angle is called the:

  1. Hypotenuse

  2. Adjacent Side

  3. Opposite Side


Correct Option: C
Explanation:

The side opposite the right angle is called the opposite side.

In a right triangle, the side adjacent to the right angle is called the:

  1. Hypotenuse

  2. Adjacent Side

  3. Opposite Side


Correct Option: B
Explanation:

The side adjacent to the right angle is called the adjacent side.

The side opposite the right angle in a right triangle is always:

  1. Shorter than the hypotenuse

  2. Longer than the hypotenuse

  3. Equal to the hypotenuse


Correct Option: A
Explanation:

The opposite side in a right triangle is always shorter than the hypotenuse.

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the:

  1. Adjacent and Opposite Sides

  2. Opposite and Hypotenuse Sides

  3. Adjacent and Hypotenuse Sides


Correct Option: A
Explanation:

The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the adjacent and opposite sides.

The Pythagorean Theorem is often written as:

  1. $a^2 + b^2 = c^2$

  2. $a^2 - b^2 = c^2$

  3. $a^2 + b^2 = c$


Correct Option: A
Explanation:

The Pythagorean Theorem is often written as $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the adjacent and opposite sides, respectively, and $c$ is the length of the hypotenuse.

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

  1. 8 cm

  2. 4 cm

  3. 12 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $6^2 + b^2 = 10^2$. Solving for $b$, we get $b = 8$ cm.

In a right triangle, if the length of the hypotenuse is 13 cm and the length of the opposite side is 5 cm, what is the length of the adjacent side?

  1. 12 cm

  2. 6 cm

  3. 10 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 5^2 = 13^2$. Solving for $a$, we get $a = 12$ cm.

A right triangle has an adjacent side of length 8 cm and an opposite side of length 6 cm. What is the length of the hypotenuse?

  1. 10 cm

  2. 14 cm

  3. 12 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $8^2 + 6^2 = c^2$. Solving for $c$, we get $c = 10$ cm.

If the hypotenuse of a right triangle is 20 cm and the opposite side is 12 cm, what is the length of the adjacent side?

  1. 16 cm

  2. 8 cm

  3. 14 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 12^2 = 20^2$. Solving for $a$, we get $a = 16$ cm.

In a right triangle, if the length of the hypotenuse is 17 cm and the length of the adjacent side is 8 cm, what is the length of the opposite side?

  1. 15 cm

  2. 12 cm

  3. 10 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $8^2 + b^2 = 17^2$. Solving for $b$, we get $b = 15$ cm.

A right triangle has an adjacent side of length 10 cm and a hypotenuse of length 26 cm. What is the length of the opposite side?

  1. 24 cm

  2. 16 cm

  3. 18 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $10^2 + b^2 = 26^2$. Solving for $b$, we get $b = 24$ cm.

If the opposite side of a right triangle is 7 cm and the hypotenuse is 13 cm, what is the length of the adjacent side?

  1. 12 cm

  2. 8 cm

  3. 10 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 7^2 = 13^2$. Solving for $a$, we get $a = 12$ cm.

In a right triangle, if the length of the hypotenuse is 25 cm and the length of the opposite side is 20 cm, what is the length of the adjacent side?

  1. 15 cm

  2. 10 cm

  3. 12 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 20^2 = 25^2$. Solving for $a$, we get $a = 15$ cm.

A right triangle has an opposite side of length 9 cm and a hypotenuse of length 15 cm. What is the length of the adjacent side?

  1. 12 cm

  2. 6 cm

  3. 8 cm


Correct Option: A
Explanation:

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 9^2 = 15^2$. Solving for $a$, we get $a = 12$ cm.

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