Question
If a right triangle has sides 5, 12, and 13 units, then a triangle with sides 10, 24, and 26 is also a right triangle.(1 point)
Responses
True, because multiples of a right triangle triple produces a similar right triangle with congruent angles.
True, because multiples of a right triangle triple produces a similar right triangle with congruent angles.
False, because doubling the sides of the triangle does not keep the angles congruent
False, because doubling the sides of the triangle does not keep the angles congruent
Responses
True, because multiples of a right triangle triple produces a similar right triangle with congruent angles.
True, because multiples of a right triangle triple produces a similar right triangle with congruent angles.
False, because doubling the sides of the triangle does not keep the angles congruent
False, because doubling the sides of the triangle does not keep the angles congruent
Answers
GPT-4o mini
The correct response is:
**True, because multiples of a right triangle triple produce a similar right triangle with congruent angles.**
When you scale the sides of a right triangle by a constant factor (in this case, doubling), the resulting triangle maintains the same angles and thus remains a right triangle. The side lengths are scaled proportionally, and since 5, 12, and 13 form a right triangle, scaling these sides by a factor of 2 (to 10, 24, and 26) will also form a right triangle.
**True, because multiples of a right triangle triple produce a similar right triangle with congruent angles.**
When you scale the sides of a right triangle by a constant factor (in this case, doubling), the resulting triangle maintains the same angles and thus remains a right triangle. The side lengths are scaled proportionally, and since 5, 12, and 13 form a right triangle, scaling these sides by a factor of 2 (to 10, 24, and 26) will also form a right triangle.