Question

Which set of side lengths shows similar triangles?
a) Triangle ABC : 40, 20, 50; Triangle XYZ: 10, 12.5, 10
b) Triangle ABC : 30, 20, 30; Triangle XYZ: 40, 30, 20
c) Triangle ABC : 110, 80, 60; Triangle XYZ: 12, 16, 22
d) Triangle ABC : 32, 20, 32; Triangle XYZ: 40, 26, 26

Answer 1

a) Triangle ABC : 40, 20, 50; Triangle XYZ: 10, 12.5, 10
XYZ has two equal sides 10 and 10. But ABC has no equal sides. So the triangles are not similar.

b) Triangle ABC : 30, 20, 30; Triangle XYZ: 40, 30, 20
ABC has two equal sides 30 and 30. But XYZ has no equal sides. So the triangles are not similar.

Answer 2

c) Triangle ABC : 110, 80, 60; Triangle XYZ: 12, 16, 22
The highest side length of ABC is 110.
The highest side length of XYZ is 22.
The ratio is 110 / 22 = 5

The second highest side length of ABC is 80.
The second highest side length of XYZ is 16.
The ratio is 80 / 16 = 5

The ratio of the third side is: 60 / 12 = 5

Since all three sides have the same ratio, the two triangles are similar.

Answer 3

ooooooh i see what it is now thank you

Answer 4

d) Triangle ABC : 32, 20, 32; Triangle XYZ: 40, 26, 26
The biggest sides are 32 and 32 of triangle ABC but the smallest two sides are 26 and 26. So they cannot be similar. So it is not D.

You are welcome.