Which set of side lengths shows similar triangles?


Triangle ABC : 40, 20, 50; Triangle XYZ: 10, 12.5, 10
Triangle ABC : 30, 20, 30; Triangle XYZ: 40, 30, 20
Triangle ABC : 110, 80, 60; Triangle XYZ: 12, 16, 22
Triangle ABC : 32, 20, 32; Triangle XYZ: 40, 26, 26

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The set of side lengths that shows similar triangles is:

Triangle ABC: 40, 20, 50
Triangle XYZ: 10, 12.5, 10

To determine which set of side lengths shows similar triangles, we need to compare the ratios of the corresponding side lengths.

For Triangle ABC : 40, 20, 50; and Triangle XYZ: 10, 12.5, 10,
the ratios of the corresponding side lengths are:
AB/XY = 40/10 = 4
BC/YZ = 20/12.5 = 1.6
AC/XZ = 50/10 = 5

For Triangle ABC : 30, 20, 30; and Triangle XYZ: 40, 30, 20,
the ratios of the corresponding side lengths are:
AB/XY = 30/40 = 0.75
BC/YZ = 20/30 = 0.67
AC/XZ = 30/20 = 1.5

For Triangle ABC : 110, 80, 60; and Triangle XYZ: 12, 16, 22,
the ratios of the corresponding side lengths are:
AB/XY = 110/12 = 9.17
BC/YZ = 80/16 = 5
AC/XZ = 60/22 = 2.73

For Triangle ABC : 32, 20, 32; and Triangle XYZ: 40, 26, 26,
the ratios of the corresponding side lengths are:
AB/XY = 32/40 = 0.8
BC/YZ = 20/26 = 0.77
AC/XZ = 32/26 = 1.23

Based on the ratios of the corresponding side lengths, the set of side lengths that show similar triangles is Triangle ABC: 30, 20, 30; and Triangle XYZ: 40, 30, 20. This is because the ratios of the side lengths in this pair are approximately equal to each other.