10. Determine whether triangle XYZ is scalene, isosceles, or equilateral. (3 points)
Hint you cannot just tell me because it looks like sides are congruent or not congruent You must use distance formula or some other method to proves sides congruent
Answer isosceles
How would I show work
To show work, you would first need the coordinates of the vertices X, Y, and Z. Let's assume the coordinates are given as X(x1, y1), Y(x2, y2), and Z(x3, y3).
1. Use the distance formula to find the length of each side of the triangle:
XY = sqrt((x2-x1)^2 + (y2-y1)^2)
YZ = sqrt((x3-x2)^2 + (y3-y2)^2)
XZ = sqrt((x1-x3)^2 + (y1-y3)^2)
2. Compare the lengths of the sides:
If all three sides are equal (XY = YZ = XZ), then the triangle is equilateral.
If only two sides are equal (either XY = YZ, YZ = XZ, or XY = XZ), then the triangle is isosceles.
If no sides are equal (XY ≠ YZ ≠ XZ), then the triangle is scalene.
3. Write down the conclusion based on the comparison above.
For example, assume the coordinates are X(1,1), Y(5,2), and Z(2,6):
XY = sqrt((5-1)^2 + (2-1)^2) = sqrt(17)
YZ = sqrt((2-5)^2 + (6-2)^2) = sqrt(20)
XZ = sqrt((1-2)^2 + (1-6)^2) = sqrt(26)
Since only two sides have equal lengths (in this case, none of the sides are equal), the triangle is scalene.
In your case, you have already determined the triangle to be isosceles, so you should find two sides with equal lengths using these steps.