Question
Order the sides of each triangle from shortest to longest.
inside triangle
Y= top corner 38 degrees
X = left bottom corner 104 degrees
z = right bottom corner 38 degrees
Question 12 options:
XZ and XY; YZ
XZ, YZ, XY
YZ and XY; XZ
XY, YZ, XZ
inside triangle
Y= top corner 38 degrees
X = left bottom corner 104 degrees
z = right bottom corner 38 degrees
Question 12 options:
XZ and XY; YZ
XZ, YZ, XY
YZ and XY; XZ
XY, YZ, XZ
Answers
GPT-4o mini
To determine the order of the sides of triangle XYZ based on the angle measures, we can use the property that the larger the angle, the longer the opposite side.
In triangle XYZ:
- \( \angle X = 104^\circ \) (opposite side YZ)
- \( \angle Y = 38^\circ \) (opposite side XZ)
- \( \angle Z = 38^\circ \) (opposite side XY)
The angles 38 degrees at corners Y and Z are equal, which means sides XZ and XY will be equal in length. However, since angle X (104 degrees) is larger than angles Y and Z (both 38 degrees), side YZ will be the longest side.
Therefore, we can order the sides based on the angles opposite them:
- The shortest side will be XZ (opposite to angle Y).
- The next longest side will be XY (opposite to angle Z).
- The longest side will be YZ (opposite to angle X).
Putting these together, the order from shortest to longest is: **XZ, XY, YZ.**
However, based on the provided answer options, we need to note that since XZ and XY are equal in length, we consider them together.
Thus the final order from shortest to longest is: **XZ, XY (or YZ); YZ (twice).**
Looking at the options again, the best-fitting answer is:
**XZ, YZ, XY**
So, in short, the closest option to the order we've determined is: **XZ, YZ, XY.**
In triangle XYZ:
- \( \angle X = 104^\circ \) (opposite side YZ)
- \( \angle Y = 38^\circ \) (opposite side XZ)
- \( \angle Z = 38^\circ \) (opposite side XY)
The angles 38 degrees at corners Y and Z are equal, which means sides XZ and XY will be equal in length. However, since angle X (104 degrees) is larger than angles Y and Z (both 38 degrees), side YZ will be the longest side.
Therefore, we can order the sides based on the angles opposite them:
- The shortest side will be XZ (opposite to angle Y).
- The next longest side will be XY (opposite to angle Z).
- The longest side will be YZ (opposite to angle X).
Putting these together, the order from shortest to longest is: **XZ, XY, YZ.**
However, based on the provided answer options, we need to note that since XZ and XY are equal in length, we consider them together.
Thus the final order from shortest to longest is: **XZ, XY (or YZ); YZ (twice).**
Looking at the options again, the best-fitting answer is:
**XZ, YZ, XY**
So, in short, the closest option to the order we've determined is: **XZ, YZ, XY.**