Geometry Problems of the Day

The following problems were taken from the GEOMETRY (COMMON CORE) Regents Exam given on Thursday, January 26, 2017.
Previous problems can be found here.

Part 1

9. The diagram shows rectangle ABCD, with diagonal BD

. What is the perimeter of rectangle ABCD, to the nearest tenth?

(2) 32.8.
You could use sin and cos to find the length and the width of the rectangle.
However, the diagonal creates a 30-60-90 right triangle, which has special properties. The side opposite the 30^o angle is half the length of the hypotenuse (the diagonal of the rectangle). The side opposite the 60^o angle is equal to the shorter side times radical 3, or (3)^(.5).
So the perimeter is 6 + 6 + 6(3)^(.5) + 6(3)^(.5) = 32.7846097, which rounds to 32.8.

10. Identify which sequence of transformations could map pentagon ABCDE onto pentagon A"B"C"D"E", as shown below.

(3) line reflection followed by a translation
Notice the position of B" and D". They indicate that one reflection took place, not a rotation. Likewise, had two reflections taken place, then B" and D" would be in different places.




Continue to the next problems.