GEOMETRY: Chapter 8

8.2: Use Proportions to Solve Geometry Problems

More Properties of Proportions

2. Reciprocal Property—If two ratios are equal, then their reciprocals are also equal.

3. If you interchange the means of a proportion, then you form another true proportion.

4. In a proportion, if you add the value of each ratio’s denominator to its numerator, then you form another true proportion.

If , then c b d

db

a

a c

If , then a a

d

c b

b c d

If , the+

n a a d

d d

c b c

b b

Ex. 1: In the diagramWrite four true proportions.

AB AC

DE DF

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 365.

Ex. 1: In the diagramWrite four true proportions.

Sample Answer 12/9 = 8/x; 9/12=x/812/8=9/x; (12+9)/9= (8+x)/x

AB AC

DE DF

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 365.

Ex. 2: In the diagram, Find ST and VT.

SV SU

VT UR

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 365.

Ex. 2: In the diagram, Find ST and VT.

Answer: 26 2/3, 18 2/3

SV SU

VT UR

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 365.

Ex. 3: The blueprint shows a scale drawing of an MP3 Music player. The diameter of the round speaker on the blueprint is 0.4 inch. The actual length is 1.6 inches. What is the scale of the blueprint?

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 366.

Ex. 3: The blueprint shows a scale drawing of an MP3 Music player. The diameter of the round speaker on the blueprint is 0.4 inch. The actual length is 1.6 inches. What is the scale of the blueprint?

Answer: 1 in: 4 in.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 366.

Ex. 4:The scale of a map is 1in.: 1440ft.Find the actual length of a street if the

distance on the map is 3 inches.

Ex. 4:The scale of a map is 1in.: 1440ft.Find the actual length of a street if the

distance on the map is 3 inches.

Answer: 3(1440ft)= 4320ft.

Ex.5: You buy a 3-D scale model of the Sears Tower in Chicago, IL. The actual height of the building, including the television antenna on top, is 1703 feet. Your model is 29.4 in tall, including the 4.4 inch antenna on top of the model.

a.What is the height of the actual antenna?b.About how many times as tall as your model

is the actual building, including the antenna?

Ex.5: You buy a 3-D scale model of the Sears Tower in Chicago, IL. The actual height of the building, including the television antenna on top, is 1703 feet. Your model is 29.4 in tall, including the 4.4 inch antenna on top of the model.

a.What is the height of the actual antenna?b.About how many times as tall as your model

is the actual building, including the antenna?

Answer: a. about 255 feet; 695 times