Geometry Problems of the Day (Geometry Regents, June 2011)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Geometry Regents, June 2011

Part II: Each correct answer will receive 2 credits. Partial credit is available.


29. Given the true statement, “The medians of a triangle are concurrent,” write the negation of the statement and give the truth value for the negation.

Answer:

You can negate the statement by adding "not" after the "are", or by preceding the sentence with "It is not the case that".

Negation: "The medians of a triangle are not concurrent."

The negation of any True statement is Not True, which is False. So this statement is False.

This may seem unfair, but if you forget to write "False", you will lose a credit. However, if you write "False" and nothing else, you will not NO credit at all. If you write an incorrect statement and "false", you will get 1 credit.

30. Using a compass and straightedge, on the diagram below of RS, construct an equilateral triangle with RS as one side. [Leave all construction marks.]

Answer:

Open your compass from R to S. Make an arc to one side of the line. Without changing the compass, center in on S and make a second arc that overlaps the first one. Using the straightedge, draw lines from the intersection of the two arcs to points R and S. You have drawn an equilateral triangle.

31. The Parkside Packing Company needs a rectangular shipping box. The box must have a length of 11 inches and a width of 8 inches. Find, to the nearest tenth of an inch, the minimum height of the box such that the volume is at least 800 cubic inches.

Answer:

Volume = length * width * height. You're given the Volume, length and width. Solve for the height.

800 = 11 * 8 * h

800 = 88h

h = 800/88 = 9.09, which rounds up to 9.1

Note that you MUST round up because it says at least. If you rounded down, then you wouldn't have enough.

More to come. Comments and questions welcome.

More Regents problems.

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