Geometry Regents Exam

A vertical mine shaft is modeled in the diagram below. At a point on the ground 50 feet from the top of the mine, a ventilation tunnel is dug at an angle of 47°.

• 47

• 54

• 68

• 73

Tags

CCSS.HSG.SRT.C.8

Directed line segment AJ has endpoints whose coordinates are A(5,7) and J(-10,-8). Point E is on AJ such that AE:EJ is 2:3. What are the coordinates of point E?

• (1,-1)

• (-5,-3)

• (-4,-2)

• (-1,1)

Tags

CCSS.HSG.GPE.B.6

A right circular cylinder has a diameter of 8 inches and a height of 12 inches. Which two-dimensional figure shows a cross section that is perpendicular to the base and passes through the center of the base?

• Circle with radius 4 inches

• Circle with radius 8 inches

• Rectangle with dimensions 4 inches by 12 inches

• Rectangle with dimensions 8 inches by 12 inches

Tags

CCSS.7.G.A.3

On the set of axes below, AB is drawn and passes through A(-2,6) and B(4,0).

• y = -x + 4

• y = -x + 2

• y = -1/2x + 4

• y = -1/2x + 2

In parallelogram ABCD with AC ⊥ BD, AC = 12 and BD = 16. What is the perimeter of ABCD?

• 10

• 24

• 40

• 56

Tags

CCSS.HSG.CO.C.11

A sandbox in the shape of a rectangular prism has a length of 43 inches and a width of 30 inches. Jack uses bags of sand to fill the sandbox to a depth of 9 inches. Each bag of sand has a volume of 0.5 cubic foot. What is the minimum number of bags of sand that must be purchased to fill the sandbox?

• 14

• 13

• 7

• 4

Tags

CCSS.7.G.B.6

Parallelogram EATK has diagonals ET and AK. Which information is always sufficient to prove EATK is a rhombus?

• EA ⊥ AT

• EA ≅ AT

• ET ≅ AK

• ET ≅ AT

Triangles YEG and POM are two distinct non-right triangles such that ∠G ≅ ∠M. Which statement is sufficient to prove ΔYEG is always congruent to ΔPOM?

• ∠E ≅ ∠O and ∠Y ≅ ∠P

• YG ≅ PM and YE ≅ PO

• There is a sequence of rigid motions that maps ∠E onto ∠O and YE onto PO.

• There is a sequence of rigid motions that maps point Y onto point P and YG onto PM.

Tags

CCSS.HSG.SRT.B.5

A small town is installing a water storage tank in the shape of a cylinder. The tank must be able to hold at least 100,000 gallons of water. The tank must have a height of exactly 30 feet. [1 cubic foot holds 7.48 gallons of water] What should the minimum diameter of the tank be, to the nearest foot?

• 12

• 24

• 65

• 75

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

In isosceles triangle ABC shown below, AB ≅ AC, and altitude AD is drawn. The length of AD is 12 cm and the length of BC is 10 cm. Determine and state, to the nearest cubic centimeter, the volume of the solid formed by continuously rotating △ABC about AD.

Tags

CCSS.HSG.MG.A.1