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) TopLeft Small 16 x Big SmallBig Top Left x 18 = x 18 = 16 x x = 288  Simplify. 24 x =  Cross products are equal  24 x = =  Divide both sides by x x = 12  Simplify.

PRE-ALGEBRA Trapezoid ABCD ~ trapezoid EFGH. Find the value of k. 3 k = 6 2Write cross products. = Divide each side by 3. 3k k = 4Simplify. Similar Figures and Scale Drawings LESSON 6-3 Additional Examples TopBottom Big 6 3 Small k 2 BigSmall Top 6 k Bottom 3 2 3k = 12Simplify.

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) WomanTree Shadow (Bottom) 4 10 Height (Right) 5 h 4h = 50  Simplify. 4 h = 10 5  Cross products are equal =  Divide both sides by 4.. 4h 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 x 1.5 = x = 10 Simplify. The flagpole is 10 ft tall. Similar Figures and Scale Drawings LESSON 6-3 Additional Examples RightBottom Bigx5 Small31.5

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 x = 66  Simplify. 1 x =  Cross products are equal  1 x = 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.) d3d map (distance) (in.) actual (distance) (mi.) = Write a proportion. 1 d = 24 3Write cross products. d = 72Simplify (Identity Property). Similar Figures and Scale Drawings LESSON 6-3 Additional Examples InchesMiles Known124 Unknown3d KnownUnknown Inches13 Miles24d

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 Drawings LESSON 6-3