*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

*and*

**sin***to find the length and the width of the rectangle.*

**cos**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.

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