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Terms in this set (25)

1 ▶︎▶︎▶︎ MEANS-EXTREMES PROPERTY, or CROSS-PRODUCTS PROPERTY (also known as Property 1):

➜ If a/b = c/d, then a • d = b • c.

➜ Conversely, if a • d = b • c, and neither a • d nor b • c equals zero, then a/b = c/d and b/a = d/c

For example, for the proportion 8/10 = 4/5,
the Means-Extremes Property (Property 1) specifies 8 • 5 = 10 • 4, or 40 = 40.

2 ▶︎▶︎▶︎ MEANS OR EXTREMES SWITCHING PROPERTY (also known as Property 2):

➜ If a/b = c/d and is a proportion, then both d/b = c/a and a/c = b/d are proportions.

For example, for the proportion 8/10 = 4/5,
the Means or Extremes Switching Property (Property 2) specifies that if you were to switch the 8 and 5 or switch the 4 and 10, then the new statement is still an accurate proportion.

If 8/10 = 4/5, then 5/10 = 4/8, OR if 8/10 = 4/5, then 8/4 = 10/5.

3 ▶︎▶︎▶︎ UPSIDE-DOWN PROPERTY (also known as Property 3):

➜ If a/b = c/d, then b/a = d/c.

For example, if 9 • a = 5 • b, and the product ≠ 0, then find the ratio for a/b.

First, apply the converse of the Cross Products Property and obtain 9/5 = b/a.

Next, proceed in one of the following two ways:
☛ Apply Property 3 to 9/5 = b/a:
Turn each side upside-down.
5/9 = a/b, or a/b = 5/9

☛ Apply Property 2 to 9/b = 5/a:
Switch the 9 and the a, so that a/b = 5/9

4 ▶︎▶︎▶︎ DENOMINATOR ADDITION/SUBTRACTION PROPERTY (also known as Property 4):

➜ If a/b = c/d, then (a + b)/ b = ( c + d)/ d or (a − b)/ b = (c − d)/ d.

Copy and paste the following link into your browser to learn more about using the four properties of proportion in geometry:

https://youtu.be/fvtlFmRA5sY
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