Competency 004: geometry and measurement

Use the Diagram below to answer the questions that follows. Assume triangle ABC is similar to DEF. If AC is 10, DF is 5 and DE is 4, what is the length of AB?

A. 8 Explanation: When triangles are similar, their corresponding sides are proportional. For these two triangles we have: Large :AB = AC = BC ----------------------- Small: DE DF EF

Use the letters below to answer the question that follows. E T V D Students are classifying the letters of the alphabet according to the type of symmetry they have. Which of the following letters has the same kind of symmetry as the letters shown above?

A. M Explanation: A figure is symmetrical when one side of the figure is the mirror image of the other side. If you were to put a line of symmetry in the middle of the letter "M" shown above, you would be able to see that both sides are symmetrical. The same is true for the letters listed below: A B C D E H I M O T U V W X Y Note that sometimes the mirrors are on the right of the letters and sometimes on the tops (or bottoms) to get the same reflected image.)

An individual from Texas is interested in purchasing land in Canada. The realtor informs him that there is a piece of land that is 1.8 km^2. The individual is lost as the size of the piece of land. He needs to be able to convert the 1.8 km^2 to square miles. Convert 1.8 km^2 to square miles for the Texan (using 1 square mile = 2.6 square kilometers).

B. 0.69 square miles Explanation: (image)

A third-grade class is using plaster of Paris to make impressions of their hands. Each student needs 12 ounces of plaster to make an impression of their hands. There are a total of 20 students in the class. How many pounds of plaster will the teacher need for the activity?

B. 15 Pounds Explanation: It takes 12 ounces of plaster per impression. Since there are 20 students, then it will take 20 x 12 = 240 ounces of plaster to make all the impressions. The answer choices are all given in pounds (Ib) not ounces (oz). The next step is to convert 240 ounces to pounds. Using the conversion that 1 pound is equivalent to 16 ounces: 1Ib. = 16 oz. convert ounces to pounds dividing 240 oz. by 16oz. 240/16 = 15 Ib.

Find the measure of x.

B. 52 degrees Explanation: The bottom left angle of the triangle is 35 degrees derived by subtracting 145 degrees from the triangle is 93 degrees, since the vertical angle of 93 degrees is above it. Since all angles of the triangle 93 degrees from 180 degrees gives 52 degrees for the bottom right angle.

Sea-tac Airport in Seattle, WA, has a flight leaving for Dallas, TX every 2 hours and a flight leaving for Washington, D.C. every 45 minutes. At 5:00 A.M., on Monday, a flight to Dallas and a flight to Washington, D.C. leave at the same time. What is the next time that flights to Dallas and Washington, D.C. will leave at the same time?

B. Answer: 11:00 A.M. the same day Explanation: Convert 2 hours into 120 minutes. Factor both numbers into prime numbers: (45 = 3

A popcorn company needs to have a new side label printed for their large popcorn holiday can. The side label will cover the entire surface area of the cylinder part from top to bottom. The diameter of the can is 16 inches and the height is 20 in. How much area does the new label cover?

C. 1005.31 in^2 Explanation: Given the diameter is 16, the radius is half of that. The circumference is C= 2piR = 2piR(8)= 50.265. The surface area is the product of the circumference and the height: 50.2655 x 20 =1005.31 in ^2.

Use the following information below to answer the question that follows. Students in Mr. Stephen's forth-grade class are working on a project for the cross-country team involving motion in one dimension. The graph below illustrates the velocity of a member of the cross-country team running in a straight line. The data was collected at 2-second intervals for 20 seconds. If Mr. Stephen's students wanted to provide an estimate of the total distance the runner has run between 0 and 12 seconds which of the following approaches should they use?

C. Determine the area that is under the curve between 0 to 12 seconds. Explanation: To answer this question you would need to multiply the rate (velocity) of running by the time the runner is running, or d = rt. (d= distance, r=velocity, and t= time). During the interval for t= 0 to t= 12 you should multiply the average velocity during this time period by the length of the interval, 12- 0 = 12 seconds. Geometrically, this can be represented by the area of a triangle with a height equal to the velocity at 12 seconds (approx. 3) and a base of 12s under the curve formed between t=0s and t= 12s. To arrive at an est. of the total distance run by the cross country runner, you should add the distance covered during each of the two second intervals between 0 and 12 seconds, inclusive. This would equal to the area of the curve between 0 and 12 seconds on the graph.

The following net is for a _____.

C. Hexagonal Pyramid Explanation: There are 6 sides to the figure in this net and it forms a point, so it is a hexagonal pyramid.

Since the area of a rectangle is A = L x W, what is the area of a triangle?

C. LW/2 Explanation: The area of a triangle is A = 1/2LW. This choice is mathematically the same.