Unit 1 Study Guide7th Grade

Information

• The exam will be on Friday, October 16th. I will e-mail a link to all students and share the link in class as well.

• The exam will close at 4:00pm on Friday. If the exam has not been turned in at that time, it will be recorded as a 0.

• In this document are examples of problems you might encounter and definitions you should be familiar with.

• After class on Thursday, a new document will be uploaded here which will contain the answers discussed in class.

• This does not necessarily cover everything that could appear on the exam. I would suggest looking over note, your work in the book, etc. as well.

Scaled Copies

1. Know, in general, what a scaled copy is and be able to determine if a copy if a scaled copy of the original.

2. If given an original figure and a scaled copy of it, be able to determine what the scale factor is.

3. If given an original figure and a scale factor, be able to determine what the measurements of side lengths and angles in the scaled copy.

QUESTION #1

On the right, we have an original figure and a copy of it.

(1) Is the copy a scaled copy? Explain.

QUESTION #1 (ANSWER)

• Figure 1 is not a scaled copy of the original.

• The height and width (measured at the bottom) of the original are both 2 units. In Figure 1, the width remains 2 units. However, the height is now 3 units. For this to be a scaled copy, the original lengths must be multiplied by the same number which did not happen here.

QUESTION #2 & #3

Quadrilateral EFGH is a scaled copy of ABCD.

(2) If Angle CDA (marked in red) measures 40 degrees, what is measurement of Angle GHE (marked in blue)? Explain.

(3) Using the information given, what is the measurement of the side GF? Explain.

QUESTION #2 & #3 (ANSWERS)

• If Angle CDA measures 40 degrees, Angle GHE is also 40 degrees. Remember angles in a scaled copy do NOT change!! ☺

• The length of GF is 8. On the top, the original 6 in length while the copy is 12 in length. This means the copy is twice as large. So we double side CB and get 8.

QUESTION #4

Triangle D is a scaled copy of Triangle O.

(4) What is the scale factor from Triangle O to Triangle D?

QUESTION #4 (ANSWER)

• The scale factor from Triangle O to Triangle D is ½.

• Triangle D is half the size of Triangle O. Recall that the scale factor is always the number we multiply by. Thus, the scale factor is ½ as multiplying by ½ is the same as dividing by 2.

QUESTION #5

(5) Which of the following is true?

A. If the scale factor is 3, we add 3 to each side length of the original to get the scaled copy.

B. If the scale factor is ½, the angles in the scaled copy are half the size of the original.

C. A scaled copy could be exactly the same size as the original.

D. The scaled copy is always larger than the original.

E. The scaled copy could have more sides than the original figure.

F. If two polygons have the same angle measures for all angles, then one must be a scaled copy of the other.

QUESTION #5 (ANSWER)

• Choice C is correct. If the copy is the same exact size, the scale factor is 1.

• Choice A is incorrect as we never add to get a scaled copy. We multiplyonly!

• Choice B is incorrect because ANGLES NEVER CHANGE in scaled copy!

• Choice D is incorrect because the copy would be smaller if the scale factor is a number between 0 and 1 (for example, ½). We saw this in Question #4.

• Choice E is incorrect because the figure must be the same shape and must have the same number of sides.

• Choice F is incorrect. Consider a square with sides of length 2. Then consider a rectangle with sides of length 2 and 3. Both the square and rectangle have four 90 degree angles. However, the rectangle is not a scaled copy of the square (as you cannot just change the length of some sides).

Corresponding Parts (Points, Sides, Angles, Etc.)

1. Be able to identify corresponding parts given an original figure and its scale copy.

QUESTION #6

Polygon 2 is a scaled copy of Polygon 1.

(6) In Figure 2, what is the corresponding angle to Angle BAF?

QUESTION #6 (ANSWER)

• The corresponding angle to Angle BAF is Angle HGL.

• Notice how H is in the same position as B, G the same position as A, and L the same position as F. We simply need to make sure our corresponding angle is in the same order as the original. (No calculations required ☺)

Unit Price

1. Understand what unit price is and how to calculate it.

2. Be able to use the unit price to find the price of a given number of items.

QUESTION #7 & #8

Mr. Morrison is buying penguins to keep under his desk. He purchases 6 penguins for $133.50.

(7) What is the unit price for these penguins? In other words, how much is a single penguin?

(8) How much would 13 penguins cost?

QUESTION #7 & #8 (ANSWER)

• The unit price for these penguins is $22.25. To find this, we can

divide the total cost by the number of penguins. $133.50

6 𝑝𝑒𝑛𝑔𝑢𝑖𝑛𝑠= $22.25

• The cost of 13 penguins would be $289.25. To find this, we can multiple the unit price above by 13. $22.25 ∙ 13 = $289.25

QUESTION #9

QUESTION #9 (ANSWER)

• Choices B, C, D, and F must be true.

• Choice A is false as it is always possible to have side lengths that are not whole numbers.

• Choice B is true because all angles are whole numbers in the original and will not change.

• Choice C is true because P has one right angle so any copy will as well.

• Choice D is true as we always multiple the side lengths by the scale factor.

• Choice E is false because ANGLES NEVER CHANGE in a scaled copy.

• Choice F is true because P has 2 acute (40, 80) and 3 obtuse (125, 250, 135) angles. So, any copy would have the same measurements.

Scale Drawings

1. Know what a scale drawing is.

2. Be able to use a scale to find distance in actual place/object or in the scaled drawing/map.

3. Be able to find what the scale is and represent it in different ways.

QUESTION #10, #11, and #12

Madison is drawing a map of Spokane and the surrounding communities. She decides that a distance of 7 miles will be represented by 2 inches on her drawing.

(10) What scale is Madison using for her map?

(11) What is another way to represent her scale?

(12) If a road measures 18 miles in length, how long would it appear on Madison’s map?

QUESTION #10, #11, and #12 (ANSWERS)

• The scale Madison is using is “2in to 5mi”. You could have an equivalent scale here and still be correct.

• Possible equivalent scales would include “1in to 2.5mi” or “0.4in to 1mi” or “4in to 10mi”. If you multiply (or divide) both values in the original scale by any value, you will have an equivalent scale. However, you need to have the inch (map) measurement listed first.

• An 18 mile long road would measure about 5.143 inches (or exactly 36/7 inches) on Madison’s map. The calculations, shown on the right, are done as I have done them in our notes previously. In this case, we multiply by 18/7 or about 2.571 on each side.

• Note: This problem is more difficult than what may appear on the exam. I simply wanted to put some additional challenge here.