Which statement explains the Pythagorean Theorem?(1 point) Responses 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 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
9 answers
If a triangle is a right triangle, then the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Does the Pythagorean Theorem apply to this triangle? How do you know? (1 point) Responses No, because the angle at point F is 90°. No, because the angle at point F is 90 degrees
no because the triangle is not a right triangle
yes because you can use the pythagoren theorem on any triangle yes because it is a right triangle
no because the triangle is not a right triangle
yes because you can use the pythagoren theorem on any triangle yes because it is a right triangle
The correct response is: No, because the triangle is not a right triangle. The Pythagorean Theorem only applies to right triangles, which have one angle measuring 90 degrees.
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point) No, because 369 is not equal to 100. No, because 369 is not equal to 100. No, because 244 is not equal to 225.No, because 325 is not equal to 144. No, because 325 is not equal to 144. No, because 22 is not equal to 15.
To determine if the triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. According to the converse, if the square of the longest side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Let's check if this condition holds true for the given triangle:
Longest side: 15
Other sides: 10 and 12
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
Let's check if this condition holds true for the given triangle:
Longest side: 15
Other sides: 10 and 12
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
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 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 leg length of 24.
If the equation 182 + b^2 = 302 is found to be true, we can use it to determine information about the triangle.
By rearranging the equation, we get b^2 = 302 - 182 = 120.
Now, if we take the square root of both sides, we get b = √120 = 10√3.
Therefore, if this equation is true, we know that the triangle is a right triangle, and one of the legs has a length of 10√3.
By rearranging the equation, we get b^2 = 302 - 182 = 120.
Now, if we take the square root of both sides, we get b = √120 = 10√3.
Therefore, if this equation is true, we know that the triangle is a right triangle, and one of the legs has a length of 10√3.
What is a converse of a theorem that is an if-then statement?(1 point) Responses The two parts are negated by using the word not. The if part and the then part switch places. The if part and the then part switch places. 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 that is an if-then statement is: The if part and the then part switch places.
In other words, if the original theorem states "If A then B," the converse of that theorem would be "If B then A." The converse explores the possibility that if the conclusion is true, then the hypothesis must also be true. It is important to note that the converse of a theorem may or may not be true.
In other words, if the original theorem states "If A then B," the converse of that theorem would be "If B then A." The converse explores the possibility that if the conclusion is true, then the hypothesis must also be true. It is important to note that the converse of a theorem may or may not be true.