Unit 6: Measurement & Similar Figures Study Guide
Vocabulary:
1. Customary System – The measurement system used in the U.S.
2. Metric System – The measurement system which is universally used throughout the world and is decimal based
3. Ratio – A comparison of two quantities (using division)
4. Proportion – An equation which states two ratios are equal
5. Scale Drawing – A drawing which uses a scale to make an object proportionally smaller or larger; ex. a map, a blueprint, a model car
6. Similar Figures – Figures with the same shape, but different size; the sides are proportional & the angles are congruent (equal)
7. Corresponding Parts of Similar Figures – The sides in similar figures which are in the same position as one another
TEST TIPS
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· BE SURE YOU CAREFULLY READ THE ENTIRE QUESTION BEFORE WRITING YOUR FINAL ANSWER – BE SURE TO ANSWER THE QUESTION BEING ASKED. There might be questions on the test which address perimeter or area!
· CHECK ANSWERS TO MAKE SURE THEY ARE LOGICAL.
· USE THE PROPORTION BOX METHOD
(see below for a scale drawing/map example and a similar figures/indirect measurement example)
‘ “
d s
(drawing) (small)
a b
(actual) (big)
Remember you can use the small to big proportion box for all problems, but some of you preferred to use the drawing to actual for scale drawings and maps….it is your choice. You also don’t have to use the box part of it if you don’t want, but you should be setting up a proportion for all problems.
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· Know how to find the missing angle measurement in similar figures - corresponding angles are equal
· All three angles in a triangle add up to equal 180°
· All four angles in a rectangle and in a square are 90°
· Know how to find corresponding part of similar figures without pictures. For example:
ΔRAT~ΔHOG (this means triangle RAT is similar to triangle HOG). You know
RA ~ HO because they are listed first and second in the triangles. You also know
angle A ~ angle O because they are both in the second spots in the triangles’ names.
Customary Conversions: Use the orange study guide or flashcards if you need to study conversion factors.
Length – inch, foot, yard, mile – know how to convert from/to all units
Weight – ounce, pound, ton – know how to convert from/to all units
Capacity (liquid) – fluid ounce, cup, pint, quart, gallon – know how to convert
from/to all units (you can also use the big “G”)
Proportion Method:
Convert 3 miles to feet cross-multiply & divide
miles 1 3 5,280 x 3 = 15,840, then divide by 1
feet 5,280 x 15,840/1 = 15,840 feet
Metric Conversions: Use your orange study guide to help if needed.
Length – “Meter” is the base (anything with a prefix and “meter” is length)
Weight – “Gram” is the base (anything with a prefix and “gram” is weight)
Capacity – “Liter” is the base (anything with a prefix and “liter” is capacity)
* You can just move the decimal if you know the prefixes in order…
kilo hecto deka base deci centi milli
*If you are converting from milligrams to grams, you are moving 3 spaces to the left, so you will move the decimal 3 spaces to the left.
Example: 98 mg = .098 g (I moved the decimal 3 spots to the left)
Common Metric Conversions:
1 m = 100 cm 1 m = 1000 mm 1 km = 1000 m
1 km = 100,000 cm 1 km = 1,000,000mm
meters (m) in all of the above conversions can be replaced with grams (g) or liters (L)
* Proportion Method:
Convert 98 mg to grams cross-multiply & divide
1 g x g 98 x 1 = 98, then divide by 1000
1,000 mg 98 mg 98/1000 = .098 gram
Ruler – Know how to use a ruler to measure in both customary and metric
Examples:
If an 8-foot tree casts a 2-foot shadow, how tall is the building next to the tree which casts a 16-foot shadow?
1. Draw a picture to represent the tree & its shadow and the building & its shadow
2. Find the corresponding parts of the two similar triangles (the two shadows correspond, so you can put one ‘ on each & the two heights corresponds, so put “ on each.
3. Fill in the proportion box with the three numbers and the variable.
4. Cross-multiply & divide to solve for the tree height
5. Check to see if your answer is logical
6. Answer = 64 feet
∆ ABC ~ ∆ RST. Side AB measures 20 m. Side BC measures 25 m. If side RS measures 8 m, what is the length of side ST?
1. Draw a picture to represent the two triangles and the corresponding sides
2. From looking at the beginning statement, you should know side AB corresponds to side RS (because they are both in the first and second position). You also know side BC corresponds to side ST (because they are in the second and third positions).
3. Fill in the proportion box with the corresponding numbers and the variable
4. Cross-multiply and divide to solve for side ST
5. Check to see if your answer is logical
6. Answer = side ST = 10 meters
On a blueprint of a house, 1 inch = 4 feet. If the house width is 5.5 inches on the blueprint, how wide would the house be in real life?
1. Use the scale model proportion box (the one with drawing and actual measurements)
2. Using the given scale of 1 in = 4 ft, fill in the left side of the proportion box (1 inch is the drawing measurement and 4 feet is the actual measurement)
3. Fill in the right side of the proportion box with the drawing width of 5.5 inches.
4. Put a variable in the actual width box
5. Cross-multiply & divide
6. Check to see if your answer is logical
7. Answer = The house is 22 feet wide
The scale factor between two similar rectangles is 5:2. If the longest side of the big rectangle is 38 cm. What is the longest side of the smaller rectangle?
1. Use the small to big proportion box
2. For the left ratio, plug in the scale factor – be sure you put “2” in the small box and “5” in the big box since 5 is bigger than 2
3. For the right side ratio, substitute “38” in the appropriate spot….that would be the big box since the 38 is the measurement on the big rectangle
4. Put a variable in the small rectangle box
5. Cross-multiply and divide
6. Check to see if your answer is logical
7. Answer = The longest side of the small rectangle is 15.2 cm.