6.2 use proportions to solve geometry problems hubarth geometry
DESCRIPTION
4 x = 8 10 In the diagram, NP ST MN RS = Write four true proportions. x 4 = 10 8 = x 8 4 Ex 1 Use Properties of Proportions x x x =, or =.TRANSCRIPT
6.2 Use Proportions to Solve Geometry Problems
HubarthGeometry
Key Concepts
Reciprocal Property If two ratios are equal, then their reciprocals are also equalIf = , then =
If you interchange the means of a proportion, then you form another true proportion.If , then .
In a proportion, if you add the value of each ratios denominator to its numerator, then you form another true proportion.If , then .
4x
=810
In the diagram, NPST
MNRS =
Write four true proportions.
x4
=108
=10x
84
Ex 1 Use Properties of Proportions
8 + 10
10
4 + x
x
4 + x
x=
, or 18
10= .
Given
Property of Proportions (Property 4)
Substitution Property of Equality
Cross Products Property
Solve for x.
BEEC
BDDA
=
18 + 6
6=
x3
x 12=
6x 3(18 + 6)=
So, BA = 12 and BD = 12 – 3 = 9.
In the diagram,
Find BA and BD.
=BE + EC
EC
BD + DA
DA
Ex 2 Use Proportions with Geometric Figures
Ex 3 Find the Scale of a Drawing
To find the scale, write the ratio of a length in the drawing to an actual length, then rewrite the ratio so that the denominator is 1.
The scale of the blueprint is 2.5 cm : 1 cm.
=5 cm2 cm
=5 22 2
=2.51
The blueprint shows a scale drawing of a cell phone. The length of the antenna on the blueprint is 5 centimeters. The actual length of the antenna is 2 centimeters. What is the scale of the blueprint?
length on blueprint
length of antenna
The scale of the map at the right is 1 inch : 26 miles. Find the actual distance from Pocahontas to Algona.
Use a ruler. The distance from Pocahontas to Algona on the map is about 1.25 inches. Let x be the actual distance in miles.
Ex 4 Use a Scale Drawing
Cross Products Property
Simplify.
= 1.25 (26)x
x = 32.5
The actual distance from Pocahontas to Algona is about 32.5 miles.
1.25 in.x mi 26 mi
1 in.= distance on map
actual distance
Practice
1. In Example 1, find the value of x.
5
2. In Example 2, Find AC. BEBC
DEAC =
16
3. What If ? In Example 3, suppose the length of the antenna on the blueprint is 10 centimeters. Find the new scale of the blueprint.
5 cm 1 cm
4. Two cities are 96 miles from each other. The cities are 4 inches apart on a map. Find the scale of the map.
1 in : 24 mi