pre-algebra. lesson 6-3 warm-up pre-algebra what are “similar figures”? similar figures: figures...
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PRE-ALGEBRA
PRE-ALGEBRA
Lesson 6-3 Warm-Up
PRE-ALGEBRA
What are “similar figures”?
similar figures: figures that have the same exact shape but not the same size (in other words, one figure is a bigger or smaller version of the other)
Rule: Similar figures all have:
1.Corresponding (matching) angles that have equal measures
2.Corresponding sides that are proportional to one another (ratio of matching sides is equal).
Note: The symbol means “is similar to”
Example:ABC XYZ
Similar Figures and Scale Drawings (6-3)
PRE-ALGEBRA
How do you solve a similar figures problem?
To solve a similar figures problem, set up a proportion table that includes two corresponding sides (one of the sides should be the one your looking for and the other should be one you know both measurements to)
Example:Parallelogram ABCD Parallelogram EFGH . Find x.
Similar Figures and Scale Drawings (6-3)
Top Left
Small 16 x
Big 24 18
Small Big
Top 16 24
Left x 18
=1624
x18 =
16x
2418
24x = 288 Simplify.
24 • x = 16 • 18 Cross products are equal 24 • x = 16 • 18
1
1
12
1
x = 12 Simplify.
PRE-ALGEBRA
Trapezoid ABCD ~ trapezoid EFGH. Find the value of k.
3 • k = 6 • 2 Write cross products.
= Divide each side by 3.3k3
123
k = 4 Simplify.
Similar Figures and Scale DrawingsLESSON 6-3
Additional Examples
Top Bottom
Big 6 3
Small k 2
Big Small
Top 6 k
Bottom 3 2
3k = 12 Simplify.
PRE-ALGEBRA
What is “indirect measurement”?
indirect measurement: using similar figures to figure out distances that are difficult or impossible to measure (such as tall heights).
Example:At the same exact time during the day, a tree casts a shadow 10 ft, long. and a 5 ft. woman casts a shadow 4 ft. long. How tall is the tree?
Similar Figures and Scale Drawings (6-3)
Woman Tree
Shadow (Bottom)
4 10
Height (Right)
5 h
4h = 50 Simplify.
4 • h = 10 • 5 Cross products are equal
1
1
25
2
x = 12.5 Simplify.
Height (Right)
Shadow (Bottom)
Woman 5 4
Tree h 10
The tree is 12.5 ft. tall.
PRE-ALGEBRA
A flagpole casts a shadow 5 ft long. At the same time, a
yardstick casts a shadow 1.5 ft long. The triangle shown for the
flagpole and its shadow is similar to the triangle shown for the
yardstick and its shadow. How tall is the flagpole?
1.5x = 5 • 3 Write cross products.
Divide each side by 1.5.1.5x1.5
= 5 • 31.5
x = 10 Simplify.
The flagpole is 10 ft tall.
Similar Figures and Scale DrawingsLESSON 6-3
Additional Examples
Right Bottom
Big x 5
Small 3 1.5
PRE-ALGEBRA
What is a “scale drawing”?
What is “scale”?
scale drawing: an enlarged or reduced drawing that is similar to the actual object or place (Example: a map, a scale model).
scale: the ratio of the distance in the drawing to the corresponding actual distance (Example: a map’s scale is the distance of 1 unit, such as an inch, to the actual distance in miles).
Example: The scale of a map is 1 in.:44 mi. (or 1:44). About how far is Sacramento from Santa Rosa if it’s 1.5 in. between the two cities?
Similar Figures and Scale Drawings (6-3)
In. Mi.
Known (Scale)
1 44
Unknown (Distance)
1.5 x
Known (Scale)
Unknown (Distance)
Mi. 44 x
In. 1 1.5
1x = 66 Simplify.
1 • x = 1.5 • 44 Cross products are equal 1 • x = 44 • 1.5
x = 12 Identity Property (1x = x)
Sacramento is about 66 miles from Santa Rosa.
PRE-ALGEBRA
The scale of a map is 1 in. : 24 mi. About how far is it
between two cities that are 3 in. apart on the map?
It is about 72 mi between the two cities.
map (scale) (in.)actual (scale) (mi.)
124
3d
map (distance) (in.)actual (distance) (mi.)= Write a proportion.
1 • d = 24 • 3 Write cross products.
d = 72 Simplify (Identity Property).
Similar Figures and Scale DrawingsLESSON 6-3
Additional Examples
Inches Miles
Known 1 24
Unknown 3 d
Known Unknown
Inches 1 3
Miles 24 d
PRE-ALGEBRA
Solve.
1. Parallelogram ABCD ~ parallelogram EFGH. Find the value of x.
2. A girl who is 4 feet tall casts a shadow that is 6 feet long. The tree next to her casts a shadow that is 12 feet long. How tall is the tree?
3. The scale on a map is 3 in. : 100 mi. What is the actual distance between two towns that are 9 in. apart on the map?
12
8 ft
300 mi
Lesson Quiz
Similar Figures and Scale DrawingsLESSON 6-3