Which statement explains the Pythagorean Theorem?(1 point)

Question

Responses

If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side.
If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side.

If the interior angles of a triangle add up to 180°, then the sum of the legs of the triangle is equal to the square of the hypotenuse.
If the interior angles of a triangle add up to 180 degrees , then the sum of the legs of the triangle is equal to the square of the hypotenuse.

If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.

If all angles in a triangle are of equal measure, then the length of all sides will be equa

Answer 1

The correct statement that explains the Pythagorean Theorem is:

If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.

This can be expressed mathematically as \(a^2 + b^2 = c^2\), where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides (legs) of the triangle.

Answer 2

Use the image to answer the question.

A triangle has the vertices labeled upper E upper F upper D. The height upper E upper F is labeled 15, the base upper D upper F is labeled 20, and the hypotenuse upper D upper E is labeled 25. Angle upper E measures 60 degrees and angle upper D measures 30 degrees.

Does the Pythagorean Theorem apply to this triangle? How do you know?

(1 point)
Responses

Yes, because you can use the Pythagorean Theorem on any triangle
Yes, because you can use the Pythagorean Theorem on any triangle

No, because the angle at point F is 90°.
No, because the angle at point cap f is 90 degrees .

Yes, because it is a right triangle.
Yes, because it is a right triangle.

No, because the triangle is not a right triangle.

Answer 3

The correct response is:

Yes, because it is a right triangle.

This triangle has a right angle at point F, making it a right triangle, and therefore the Pythagorean Theorem applies. The theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.

Answer 4

Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
Responses

No, because 325 is not equal to 144.
No, because 325 is not equal to 144.

No, because 22 is not equal to 15.
No, because 22 is not equal to 15.

No, because 369 is not equal to 100.
No, because 369 is not equal to 100.

No, because 244 is not equal to 225.

Answer 5

To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first need to identify the lengths as \( a = 10 \), \( b = 12 \), and \( c = 15 \) (where \( c \) is the longest side).

We then need to check if \( a^2 + b^2 = c^2 \):

• \( a^2 = 10^2 = 100 \)
• \( b^2 = 12^2 = 144 \)
• \( c^2 = 15^2 = 225 \)

Now we add \( a^2 \) and \( b^2 \):

\( 100 + 144 = 244 \)

Now we compare \( 244 \) to \( c^2 \):

\( 244 \) is not equal to \( 225 \).

Thus, the correct response is:

No, because 244 is not equal to 225.

Answer 6

If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point)
Responses

The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle, and the hypotenuse is 18.

The triangle is a right triangle, and the legs are 30 and 24.
The triangle is a right triangle, and the legs are 30 and 24.

The triangle is a right triangle with a missing side of 34.99.
The triangle is a right triangle with a missing side of 34.99.

The triangle is a right triangle with a missing leg length of 24.

Answer 7

To analyze the equation \( 18^2 + b^2 = 30^2 \):

First, let's compute \( 18^2 \) and \( 30^2 \):

• \( 18^2 = 324 \)
• \( 30^2 = 900 \)

Now we set up the equation where \( b^2 \) is the missing side:

\[ 324 + b^2 = 900 \]

Next, we can solve for \( b^2 \):

\[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

Then, we can find \( b \):

\[ b = \sqrt{576} = 24 \]

Since we confirmed that the relationship \( 18^2 + 24^2 = 30^2 \) holds true, we conclude that the triangle is a right triangle with legs of lengths 18 and 24, and the hypotenuse of length 30.

Thus, the correct response is:

The triangle is a right triangle with a missing leg length of 24.

Answer 8

What is a converse of a theorem that is an if-then statement?(1 point)
Responses

The converse is the same as the original theorem.
The converse is the same as the original theorem.

The converse of a theorem has no relationship to the original theorem.
The converse of a theorem has no relationship to the original theorem.

The two parts are negated by using the word not.
The two parts are negated by using the word not .

The if part and the then part switch places.

Answer 9

The correct response is:

The if part and the then part switch places.

In the converse of an "if-then" statement, the hypothesis (the "if" part) and the conclusion (the "then" part) are switched. For example, if the original statement is "If A, then B," the converse would be "If B, then A."

Answer 10

gyatt

Answer 11

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