Unit #1 Scale Factor

Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.

Similar Figures Two figures are similar if the measures of the corresponding angles are equal the ratios of the lengths of the corresponding sides are proportional Similar figures have the same shape but not necessarily the same size.

Finding missing angles Hint: Remember angles are the same in corresponding angles! What is angle D? <D

Finding Missing lengths 111 y ___ ____ = Write a proportion using corresponding side lengths. The cross products are equal = 100 y The two triangles are similar. Find the missing length y

y is multiplied by ,200 = 100y 22, ______ 100y 100 ____ = Divide both sides by 100 to undo the multiplication. 222 mm = y

Indirect Measurement Indirect Measurement uses similar figures and proportions to find height of objects you cannot measure directly

Word Problems 1.Underline the question 2.Set up your answer 3.Draw it out 4.Find the similar shapes in your drawing (triangles) 5.Use similar figures and proportions to solve your problem!!!!

A tree casts a shadow that is 7 ft. lawn. Ken, who is 6 ft tall, is standing next to the tree. Kens has a 2-foot long shadow. How tall is the tree? Step 1: underline the question Step 2: Set up your answer: The tree is __________tall.

Step 3: Draw it out Step 4: Find the triangles

2 7 __ 6 h = h 2 = 6 7 2h = 42 2h 2 ___ 42 2 ___ = h = 21 Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 2. Divide both sides by 2 to undo multiplication. The tree is 21 feet tall.

Example #2 Rockets

A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket? Step 1: underline the question Step 2: Set up your answer: The Rocket is __________tall.

Step 3: Draw it out Step 4: Find the triangles

____ h 4 __ = = h = 3h ___ 3h 3 ___ = 122 = h Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 3. Divide both sides by 3 to undo multiplication. The rocket is 122 feet tall.

The map shown is a scale drawing. A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object. In other words, measurements on a scale drawing are in proportion to the measurements of the real object.

Is it set up right? Why or why not? 1. The scale on the map is 3 cm: 10 m. On the map the distance between two cities is 40 cm. What is the actual distance? 2. The scale on the map is 10 in: 50. On the map the distance between two schools is 30 in. What is the actual distance?

The scale on a map is 4 in: 1 mi. On the map, the distance between two towns is 20 in. What is the actual distance? 20 in. x mi _____ 4 in. 1 mi ____ = 1 20 = 4 x 20 = 4x 20 4 ___ 4x 4 ___ = 5 = x Write a proportion using the scale. Let x be the actual number of miles between the two towns. The cross products are equal. x is multiplied by 4. Divide both sides by 4 to undo multiplication. 5 miles

Question #1 Find side GF 10 cm 5 cm 7cm 6 cm

Question #2 Determine if the ratios are proportional. Explain. No, cross proportions don’t equal (2783 doesn’t equal 3128)

Question #3 You want to leave your server a 20% tip. The total bill comes to $ How much should you leave for a tip? $10.90

Question #4 A scale on a map reads 5 in: 50 miles. If two lakes are 11 inches apart on the map, what is the actual distance? 110 Miles

Question #5 How do you know if two figures are SIMILAR? Angles are the EXACT SAME. Side lengths have to be proportionally similar

Question #6 On a sunny afternoon, a goalpost casts a 70 ft shadow. A 6 ft football player next to the goal post has a shadow 20 ft long. How tall is the goalpost?

Question #7 If all angles are congruent, are these two shapes SIMILAR Yes! The cross products are equal! 54=54 OR 3/9 is equal to 6/18 Scale Factor = 2

Question #8

Answer

Question #9 Is this a proportion? Yes! The cross products are equal! 200=200

Question #10 The following rectangles are similar. What is the length of side RS?

Question #11 A postcard is 6 inches wide and 14 inches long. When the postcard is enlarged, it is 10 inches wide. What is the length of the enlarged postcard?

Unit #2 Measurement

The customary system is the measurement system used in the United States. It includes units of measurement for length, weight, and capacity.

What is a benchmark? If you do not have an instrument, such as a ruler, scale, or measuring cup, you can estimate the length, weight, and capacity of an object by using a benchmark. It helps you visualize actual measurements!

Customary Units of Length UnitAbbreviationBenchmark Inchin.Width of your thumb FootftDistance from your elbow to your wrist YardydWidth of a classroom door milemiTotal length of 18 football fields

What unit of measure would provide the best estimate? A doorway is about 7_____________high

Customary Units of Weight UnitAbbreviationBenchmark OunceozA slice of bread PoundlbA loaf of bread TonTA small car

What unit of measure would provide the best estimate? A bike could weigh 20 _____?

Customary Units of Capacity UnitAbbreviationBenchmark Fluid ouncefl ozA spoonful CupcA glass of juice PintptA small bottle of salad dressing QuartqtA small container of paint GallongalA large container of milk

What unit of measure would provide the best estimate? A large water cooler holds about 10 _____ of water.

Customary Conversion Factors 1 foot = 12 inches 1 yard = 3 feet 1 yard = 36 inches 1 mile = 5,280 feet 1 mile = 1,760 yards 1 pound (lb) = 16 ounces (oz) 1 Ton (T) = 2,000 pounds 1 gallon = 4 quarts 1 quart= 2 pints 1 pint = 2 cups 1 cup = 8 fluid ounces (fl oz)

To convert from one unit of measurement to another unit of measurement, use a proportion Cool, we’ve been using this since November!

Important! Same measurements in the numerator Same measurements in the denominator

How many feet are in 3 miles?

A book weighs 60 ounces. How many pounds is this?

Metric System: King Henry Doesn’t Usually Drink Chocolate Milk Memorize this!

Naming the Metric Units Meter units measure Length Gram units measure mass or weight Liter units measure volume or capacity.

Length UnitAbbreviationRelation to a meterBenchmark Millimetermm.001 mThickness of a dime Centimetercm.01 mWidth of a fingernail Decimeterdm.1mWidth of a CD case Meterm1 mWidth of a single bed KilometerKm1,000 mDistance around a city block

Mass UnitAbbreviationRelation to a gram Benchmark Milligrammg.001 gVery small insect Gramg1 gLarge paper clip Kilogramkg1,000 gTextbook

Capacity UnitAbbreviationRelation to a liter Benchmark MillilitermL.001 LA drop of water LiterL1 LBlender Container

Example #1: (1) Look at the problem. 56 cm = _____ mm Look at the unit that has a number. 56 cm On the device put your pencil on that unit. k h d U d c m km hm dam m dm cm mm

Example #1: k h d U d c m km hm dam m dm cm mm 2. Move to new unit, counting jumps and noticing the direction of the jump! One jump to the right!

Example #1: 3. Move decimal in original number the same # of spaces and in the same direction. 56 cm = _____ mm Move decimal one jump to the right. Add a zero as a placeholder. One jump to the right!

Example #1: 56 cm = _____ mm 56cm = 560 mm

Question ¼ lb= ________________oz 4

Question 8 cups = ________________fl oz 16

Question 346 yards= ________________inches 12,456 inches

Question 10 quarts = ________________gal 2.5

Question An average cat weighs 15__________ (ounces, pounds, tons) Pounds

Question 130 g = ________kg.13 kg

Question What would be a reasonable measurement for the distance from NGMS to NGHS Customary Mile

Question How many pints are in a gallon? 8

Question How long is the line? 3.5 inches

Unit #3 Symmetry

A rotation is the movement of a figure around a point. A point of rotation can be on or outside a figure. The location and position of a figure can change with a rotation.

A full turn is a 360° rotation. So a turn is 90°, and a turn is 180°. 1 2 __ ° 180° 360°

Question Draw a 180 ° counterclockwise rotation

Answer Draw a 180 ° counterclockwise rotation

Question Draw a 90 ° counterclockwise rotation

Answer

Unit #3 2-D Figures

The area of a figure is the amount of surface it covers. We measure area in square units. Example: in ², cm², etc.

#1 Find the area of the figure Write the formula. Substitute 15 for l. Substitute 9 for w. A = lw A = 15 9 A = 135 The area is about 135 in in. 9 in.

A parallelogram is a quadrilateral with opposite sides that are parallel.

Base Height

AREA OF A TRIANGLE b A = 1212 bh The area A of a triangle is half the product of its base b and its height h. h

Find the area of the triangle. A = 1212 bh Write the formula. A = 1212 (20 · 12) Substitute 20 for b and 12 for h. A = 120 The area is 120 ft 2. A = 1212 (240) Multiply.

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Estimate the area of the circle. Use 3 to approximate pi. A ≈ A ≈ 1200 m m A = r 2 Write the formula for area. Replace  with 3 and r with 20. A ≈ Use the order of operations. Multiply.

Estimate the area of the circle. Use 3 to approximate pi. r = 28 ÷ 2 A ≈ m A = r 2 Write the formula for area. Replace  with 3 and r with 14. r = 14 Use the order of operations. Divide. r = d ÷ 2 The length of the radius is half the length of the diameter. A ≈ 3 196A ≈ 588 m 2 Multiply.

5 ft Question 1 Find the Area 17 ft Answer: 85 ft ²

r = 20 ÷ 2 A ≈ m A = r 2 Write the formula for area. Replace  with 3 and r with 10. r = 10 Use the order of operations. Divide. r = d ÷ 2 The length of the radius is half the length of the diameter. A ≈ 3 100A ≈ 300 m 2 Multiply. Question 2 Find the Area

Find the area of the triangle. A = 1212 bh Write the formula. A = 54 The area is 54 in 2. A = 1212 (108) Multiply. 24 ft 4 ft 1 2 A = 1212 (4 24) 1 2 Substitute 4 for b and 24 for h. 1 2 Question 3 Find the Area

Unit #4 3-D Figures

-A closed plane figure formed by three or more line segments that intersect only at their endpoints

-A three dimensional figure in which all the surfaces are polygons

-A flat surface (polygon) on a solid figure

-The segment where two faces meet

-The point where three or more edges meet

Base A side of a polygon; a face of a three dimensional figure by which the figure is measured or classified.

Prism A polyhedron that has two congruent, polygon shaped bases and other faces that are all rectangles.

Prism named after what kind of BASE it has

Pyramid A polyhedron with a polygon base and triangular sides that all meet at a common vertex.

Pyramid named after what kind of BASE it has

Cylinder A three dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface.

Cone A three dimensional figure with one vertex and one circular base.

Cube A rectangular prism with six congruent square faces.

Question What is a 3-D shape that has 5 FACES Pyramid

Which of the nets below could be used to form a pyramid like the one below? Question

54 in ²

FORMULA SHEET a=Bh Rectangular Prism: Cylinder Prism:

What is It?!?! Volume- The number of cubic units needed to ____________ a space Volume is measured in:

The figure below is a net for a cube. Suppose the square labeled 3 is the bottom face of this cube. Which number names the square that will be the front face of the cube? a. 1 b. 2 c. 5 d. 6

How many verticesdoes the rectangular prism have? How many vertices does the rectangular prism have? a. 4 b. 6 c. 8 d. 10

Find the volume of the cylinder. a in 3 b in 3 c in 3 d in 3

Find the volume of the cone. a m 3 b m 3 c m 3 d m 3

Question How many 1 inch cubes can fit in a box that is 5 inches wide, 2 inches tall and 10 inches long? 100 in ³

Question Match each situation with the appropriate units of measure. a cm 2 _______ volume of a rectangular prism b. 25 m__________ perimeter of a large square c. 5 mm__________ area of a parallelogram d ft 3 __________ length of a mosquito

Find the Surface Area 72 in ²

PRACTICE a.Top view b.Front view c.Right view