Questions

Ratios and Proportions

For the first four problems, complete the statement by filling in the blanks.

1) A ratio is a __________ of two quantities.

250 character(s) left
Your answer is too long.

2) A unit ratio is a ratio simplified to a denominator of __________.

250 character(s) left
Your answer is too long.

3) A proportion is an equation which states that two ratios are __________.

250 character(s) left
Your answer is too long.

4) Equality of Cross Products:

250 character(s) left
Your answer is too long.

5) Simplify each of the ratios:

250 character(s) left
Your answer is too long.

6) A scale model of a car has a length of 6 3/4 INCHES. The actual length of the car is 15 FEET. Comparing both measures in inches, what is the ratio of the scale length to the actual length? (Hint: 1 foot = 12 inches)

250 character(s) left
Your answer is too long.

7) On a map, three (3) inches represent 225 miles. What is the ratio of “miles to 1 inch” (a unit ratio)?

250 character(s) left
Your answer is too long.

For the next four problems, solve the proportions.

8) Solve for “x”.

250 character(s) left
Your answer is too long.

9) Solve for “x”.

250 character(s) left
Your answer is too long.

10) Solve for “x”.

250 character(s) left
Your answer is too long.

11) Solve for “x”.

250 character(s) left
Your answer is too long.

12) Solve the proportion for “y”. State the letter of the correct answer.

250 character(s) left
Your answer is too long.

13) Three angles are complementary. The ratio of their measures is 2:3:5. Find the measure of each angle.

250 character(s) left
Your answer is too long.

14) A board, 8 feet in length, is divided into two (2) boards that are cut into the ratio of 2:3. What is the length of each board?

250 character(s) left
Your answer is too long.

15) In a sampling taken at the local factory, three (3) out of every 100 CD players were defective. Based on the sample, approximately how many CD players may be defective in a shipment of 1920 CD players? Write a proportion that could be used to solve the problem, and then state the answer.

250 character(s) left
Your answer is too long.

The chart below provided conversion rates for currency throughout the world for the given date and time displayed. The chart is based on unit rates. To read the chart, find the currency that you may have in hand and the currency for which you want to exchange. For example, to exchange 200 Swiss Francs to Euro Dollars, look across the “1 Swiss Franc” row and stop in the “Euro” column, and then multiply 200 x 0.6603 to get 132.06 Euro Dollars. Use the chart to answer the next four problems. Note: All questions refer to the currency exchange rates on the date, November 22, 2004 at 7:29 am unless otherwise specified.

16) Answer the following questions: (a) What was the ratio of 1 US dollar to the Japanese Yen? (b) What was the ratio of 1 US dollar to the Euro dollar?

250 character(s) left
Your answer is too long.

17) Five hundred US dollars would have exchanged to how many AU $ (Australian dollars)?

250 character(s) left
Your answer is too long.

18) Three hundred AU $ would have exchanged to how many Yen?

250 character(s) left
Your answer is too long.

Activity: Browse to the Internet site “http://finance.yahoo.com/currency” and find the current conversion rates of the US dollar to the Euro Dollar. If this site is unavailable, you may search to find a different “currency converter” website.

19) Answer the following questions about the previous activity: (a) State the current conversion rate of the US Dollar to the Euro Dollar. (b) One hundred US dollars ($100) equals how many Euro Dollars? (c) On November 22, 2004, at 7:29 am, one hundred US dollars ($100) equaled how many Euro Dollars? (d) Comparing the US Dollar to the Euro Dollar, how has the value of the US Dollar changed?

4000 character(s) left
Your answer is too long.

Similar Polygons

For the next three problems, complete the statement by filling in the blanks.

20) Similar figures are figures that have the same shape, but are __________ in size.

250 character(s) left
Your answer is too long.

21) Similar polygons are polygons that have congruent corresponding angles and the measures of their corresponding sides are __________.

250 character(s) left
Your answer is too long.

22) The scale factor for two similar polygons is the ratio of the lengths of any two __________ sides.

250 character(s) left
Your answer is too long.

Refer to the similar quadrilaterals shown below to solve the next two problems.

23) Fill in the blanks for the following statements: (a) Angle AXY is congruent to angle _____. (b) Angle C is congruent to angle _____. (c) Angle A in quadrilateral AXYZ is congruent to angle ____ in quadrilateral ABCD.

250 character(s) left
Your answer is too long.

24) What are the missing segments for each of the proportions shown below?

250 character(s) left
Your answer is too long.

25) Refer to the diagram shown below to answer the following questions: (a) What is the value of “x”? (b) What is the value of “y”?

250 character(s) left
Your answer is too long.

In some of the following problems, you will express your answers in “radicals”. The next four problems are a review of simplifying radicals.

26) Simplify the radical.

250 character(s) left
Your answer is too long.

27) Simplify the radical.

250 character(s) left
Your answer is too long.

28) Simplify the radical.

250 character(s) left
Your answer is too long.

29) Simplify the radical.

250 character(s) left
Your answer is too long.

30) Examine the triangles shown below. (a) Are the corresponding angles of the triangles congruent? Support your answer with an explanation. (b) Are the corresponding sides proportional? Support your answer with an explanation. (c) Are the triangles similar?

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

31) Answer the following questions about the similar quadrilaterals shown in the figure below: (a) What is the value of “x”? (b) What is the value of “y”?

250 character(s) left
Your answer is too long.

Similar Triangles

32) Fill in the blanks. Postulate 20-A (AA Similarity Postulate): If _____ angles of one triangle are congruent to _____ angles of another triangle, then the triangles are similar.

250 character(s) left
Your answer is too long.

33) Refer to the scenario below to answer the following questions: (a) Why are triangles RST and VUT similar? (b) What is the height of the tree?

4000 character(s) left
Your answer is too long.

34) Write a paragraph proof to prove that triangles VWT and VUW are similar based on the information and figure shown below.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

35) Fill in the blank. Theorem 20-A (SSS Similarity Theorem): If the measures of the corresponding sides of two triangles are __________, then the triangles are similar.

250 character(s) left
Your answer is too long.

36) Apply the SSS Similarity theorem and use trial and error to examine the ratios of the various sides of the triangles. (a) Which of the two triangles are similar? (b) What is the scale factor of the two similar triangles?

4000 character(s) left
Your answer is too long.

37) Fill in the blank. Theorem 20-B (SAS Similarity Theorem): If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of a second triangle and the __________ are congruent, then the triangles are similar.

250 character(s) left
Your answer is too long.

38) Explain through the SAS Similarity Theorem how triangles FED and HEG are similar.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

39) Refer to Theorem 20-C and select the statement below that best describes similar triangles. Make sure to read all of the statements.

a.) Similar triangles are reflexive.

b.) Similar triangles are symmetric.

c.) Similar triangles are transitive.

d.) All of the above.

Applications of Similar Figures

40) Logan wants to determine the height of an electric pole in her back yard. The pole is casting a shadow of 12 feet. Her friend is five feet tall and is casting a shadow of 2 feet. Draw a picture to determine the similar triangles. (a) What is the height of the electric pole? (b) What proportion can be used to solve the problem?

250 character(s) left
Your answer is too long.

Refer to the figure below to answer the next two questions.

41) Several of the rectangles have lengths and widths that form a ratio very close to the “golden ratio” (length : width is approximately 1 : 1.618). Measure the lengths of each of the named segments in the figure. Name three rectangles that have a length-to-width ratio that approximates the “golden ratio.”

250 character(s) left
Your answer is too long.

42) Look for a pattern in the figure. To fit the pattern, where would the next rectangle be drawn? Give a specific description of its location and its appearance.

4000 character(s) left
Your answer is too long.

Extended Research: Check with your instructor to see if he/she is interested in awarding extra credit to you for writing a one-page report on the following research topic: The Divine Proportion, also called the Golden Section or Golden Ratio. You may include pictures that you find. Be sure to report all websites or other resources that you referenced to compile your report.

43) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.

No offline activities found

0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.

I do not have any Offline Activities for this unit.

Attachments

There are no attachments

Attach a File