Geometry Common Core

Which reason belongs to STEP 6?

• Isosceles Triangle Theorem

• CPCTC

• ASA

• Def. of Angle Bisector

Given a point in the coordinate plane, the rule (x, y) --> (x + 2, y - 3) translates the point in which direction? 

• 2 units to the left and 3 units up

• 3 units to the left and 2 units down

• 3 units right and 2 units up

• 2 units right and 3 units down

A rectangle is graphed on the set of axes below. A reflection over which line would carry the rectangle onto itself?

• y = 2

• y = 10

• y = 1/2 x - 3

• y = -1/2 x + 7

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°. What is the length of the tunnel, to the nearest foot?

• 47

• 54

• 68

• 73

On the set of axes below, triangle BLU has vertices with coordinates B(-3, 2), L(-2, 5), and U(1, 1). What is the area of triangle BLU?

• 11

• 12.5

• 14

• 17.1

In the diagram below, triangle CAR is mapped onto triangle BUS after a sequence of rigid motions. If AR = 3x + 4, RC = 5x – 10, CA = 2x + 6, and SB = 4x – 4, what is the length of SB?

• 6

• 16

• 20

• 28

In the diagram below, triangle GHJ is dilated by a scale factor of 1/2 centered at point B to map onto triangle CDF. If m∠DFC = 40°, what is m∠HJG?

• 20°

• 40°

• 60°

• 80°

In the diagram below of square CASH, diagonals AH and CS intersect at Z. Which statement is true?

• m∠AZC > m∠ZCH

• m∠AZC < m∠ASZ

• m∠AZC = m∠SHC

• m∠AZC = m∠ZCH

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 diameter 4

• Circle with diameter 8

• Rectangle with dimensions 4 by 12

• Rectangle with dimensions 8 by 12

In the diagram of ΔCAT below, ∠A = 90° and altitude ĀE is drawn from vertex A. Which statement is always true?

• CE / AE = AE / ET

• AE / CE = AE / ET

• AC / CE = AT / ET

• CE / AC = AC / ET