Question

select the true statement in reference to the triangles.
draw
100
124
144
draw
25
31

Explanation:

Step1: Check similarity ratio

For two triangles to be similar, corresponding sides must be in proportion. Let's check the ratios of the given sides. The first triangle has sides 100, 124, 144. The second has 25, 31, and let's find the third (let's assume corresponding sides: 100 and 25, 124 and 31, 144 and x).

Ratio of 100 to 25: $\frac{100}{25} = 4$. Ratio of 124 to 31: $\frac{124}{31} = 4$. So the scale factor is 4. Then the third side of the second triangle should be $\frac{144}{4} = 36$ (though not shown, but the ratio check for the given sides: 100/25 = 4, 124/31 = 4, so the triangles are similar by SSS similarity (if the third sides also follow the ratio) since corresponding sides are in proportion (scale factor 4). Wait, but maybe the question is about similarity. Let's confirm the ratios. 100 ÷ 25 = 4, 124 ÷ 31 = 4, so if the third side of the second triangle is 144 ÷ 4 = 36, then the sides are proportional. So the triangles are similar because their corresponding sides are in proportion (scale factor 4).

Step2: Conclusion

Since the ratios of corresponding sides (100/25 = 4, 124/31 = 4) are equal, the triangles are similar by the SSS (Side - Side - Side) similarity criterion (if the third sides also have the same ratio, which they would as 144/36 = 4). So the true statement would be that the triangles are similar because their corresponding sides are in proportion (scale factor of 4).

Answer:

The triangles are similar because their corresponding sides are in proportion (scale factor of 4). (Assuming the question is about similarity; if options were given, but since not, this is the true statement based on side ratios: 100/25 = 4, 124/31 = 4, implying similarity by SSS if third sides follow.)