All subjects an essential Ideas Parallel currently triangle polygon Perimeter and Area Similarity best Angles circles Geometric Solids coordinate Geometry

The four properties the follow are not challenging to justification algebraically, however the details will not be presented here.

You are watching: Means-extremes product property of proportions


Property 1 (Means‐Extremes Property, or Cross‐Products Property):Ifa/b=c/d, thenad =bc.Conversely, if ad = bc≠ 0, then

*
and
*
.

*

Example 1:Findaifa/12 = 3/4.

By residential property 1:

*

Example 2:Is 3 : 4 = 7 : 8 a proportion?

No. If this to be a proportion,Property 1would produce

*

Property 2 (Means or Extremes switching Property):Ifa/b=c/dand is a proportion, then bothd/b=c/aanda/c=b/dare proportions.

Example 3:8/10 = 4/5 is a proportion.Property 2says the if you were to switch the 8 and also 5 or move the 4 and also 10, then the brand-new statement is still a proportion.

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

Example 4:Ifx/5 =y/4, discover the ratio ofx/y.

*

Use the switching property of proportions and switch the means positions, the 5 and they.

*

Property 3 (Upside‐Down Property):Ifa/b=c/d, thenb/a=d/c.

Example 5:If 9a= 5b≠ 0, find the ratio

*
.

First, use the converse that theCross assets Propertyand obtain the following:

*

Next, continue in among the adhering to two ways:

ApplyProperty 3to 9/5 =b/a: revolve each side upside‐down. 5/9 =a/b, ora/b= 5/9 ApplyProperty 2to 9/b= 5/a: switch the 9 and also thea. a/b= 5/9

Property 4 (Denominator Addition/Subtraction Property):Ifa/b=c/d, climate (a+b)/b= (c+d)/dor (ab)/b= (cd)/d.

Example 6:If 5/8 =x/y, climate 13/8 = ?

*

Example 7:In Figure,AB/BC= 5/8. FindAC/BC.

*

Figure 1 Using theSegment addition Postulate.

See more: 2006 Chevy Aveo Spark Plug Gap, 2007 Chevrolet Aveo 1

Recall thatAB+BC=AC(Segment enhancement Postulate).

*

Example 8:A map is scaled so that 3 cm on the map is same to 5 really miles. If two cities on the map space 10 cm apart, what is the actual distance the cities space apart?