All topics an essential Ideas Parallel lines triangles polygon Perimeter and Area Similarity right Angles one Geometric Solids name: coordinates Geometry

The 4 properties the follow room not an overwhelming to justification algebraically, however the details will not be presented here.

You are watching: Which of the following is the means-extremes product property of proportions?


Property 1 (Means‐Extremes Property, or Cross‐Products Property):Ifa/b=c/d, thenad =bc.Conversely, if advertisement = 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 were a proportion,Property 1would produce

*

Property 2 (Means or Extremes convert 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 5 or switch the 4 and 10, climate the brand-new statement is still a proportion.

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

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

*

Use the switching residential property of proportions and also switch the method positions, the 5 and they.

*

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

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

*
.

First, use the converse of theCross products Propertyand attain the following:

*

Next, continue in one of the following two ways:

ApplyProperty 3to 9/5 =b/a: revolve each next upside‐down. 5/9 =a/b, ora/b= 5/9 ApplyProperty 2to 9/b= 5/a: move the 9 and 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, then 13/8 = ?

*

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

*

Figure 1 Using theSegment enhancement Postulate.

See more: Find The Possible Value Or Values Of Y In The Quadratic Equation 4 – 4Y – Y2 = 0.

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

*

Example 8:A map is scaled so the 3 cm on the map is equal to 5 yes, really miles. If two cities on the map space 10 cm apart, what is the actual street the cities are apart?