Regents Geometry Midterm Review

In the diagram below, congruent figures 1,2, and 3 are drawn. Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

• a reflection followed by a translation

• a rotation followed by a translation

• a translation followed by a reflection

• a translation followed by a rotation

A parallelogram must be a rectangle when its

• diagonals are perpendicular

• diagonals are congruent

• opposite sides are parallel

• opposite sides are congruent

Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have perpendicular diagonals?

• the rhombus only

• the rectangle and the square

• the rhombus and the square

• the rectangle, the rhombus and the square

Which quadrilateral has diagonals that always bisect its angles and also bisect each other?

• rhombus

• rectangle

• parallelogram

• isosceles trapezoid

Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of point P?

• (2,9)

• (0,11)

• (2,14)

• (10,2)

The diagram shows two intersecting paths within a circular garden. What is the length of the portion of the path marked x?

• 8 and 1/3

• 11

• 3

• 12

In the diagram below, tangent PA and secant PBC are drawn to circle O from external point P. If PB =4 and BC = 5, what is the length of PA?

• 20

• 9

• 8

• 6

For a circle of radius 7 feet, find the arc length s cut off by a central angle of 6 degrees

• 42 pi feet

• 7/10 pi feet

• 7/30 pi feet

• 7/15 pi feet

In the scalene triangle ABC shown in the diagram below, M< C = 90 degrees. Which equation is always true?

• sin A = Sin B

• Cos A = Cos B

• Cos A = Sin C

• Sin A = Cos B

A water cup in the shape of a cone has a height of 4 inches and a maximum diameter of 3 inches. What is the volume of the water in the cup, to the nearest tenth of a cubic inch, when the cup is filled to half its height?

• 1.2

• 3.5

• 4.7

• 14.1