What does it mean for two fractions to be equivalent? for two ratios to be equivalent?

Equivalent fractions and ratios mean that when simplified, they are the same one fraction or ratio. see examples below.

Step-by-step explanation:

For example, the fraction 1/2 is the same as 2/4 or 15/30 because when you simplify them, they are still 1/2. Therefore they are equivalent.

For example, the ratio 1:2 is the same as 5:10 or 10:20 since when broken down they all come down to 1:2. Hence they are equivalent.

Hope this answers your question.

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step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.