Regents Prep Geometry Quadrilaterals

Regents Prep Geometry Quadrilaterals Question Review

Directions: Answer all problems on a separate sheet of paper.  Remember to show all work, including all relevant formula substitutions, diagrams, graphs, charts, etc.

 1) Two consecutive angles of a parallelogram measure x and degrees respectively.  Compute the measure of the largest angle of this parallelogram.

2) Two consecutive sides of a rhombus have lengths of and respectively.  Compute the numerical value of the perimeter of this rhombus.

3) The bases of an isosceles trapezoid have length of 8 and 14, and the altitude of this trapezoid has a length of 4.  Compute the perimeter of the trapezoid.

4) Which of the following statements is not always true about a parallelogram?

  • (1) The diagonals are congruent.
  • (2) The opposite sides are congruent.
  • (3) The opposite angles are congruent.
  • (4) The opposite sides are parallel.

5) Compute the sum of the area and the perimeter of a rectangle with a base of length 12 and a diagonal of length 13.

6) In which of the following quadrilaterals are the diagonals not congruent to each other?

  • (1) isosceles trapezoid
  • (2) rhombus
  • (3) rectangle
  • (4) square

7) Which is always true of the diagonals of a parallelogram?

  • (1) They bisect each other.
  • (2) They are congruent.
  • (3) They are perpendicular.
  • (4) They bisect the angles of the parallelogram

8) Which of the following statements is false?

  • (1) All parallelograms are quadrilaterals.
  • (2) All rectangles are parallelograms
  • (3) All squares are rhombuses.
  • (4) All rectangles are squares.

9) A rectangular wall of a crate is to be built with dimensions of 16 inches and 30 inches.  To ensure that the sides of the wall form 90o angles with each other, the diagonal brace of the wall should measure

  • (1) 16 inches
  • (2) 30 inches
  • (3) 34 inches
  • (4) 46 inches

10) Which of the following best represents the perimeter of a square with a diagonal of length 10?

  • (1) 40
  • (2) 5√2
  • (3) 10√2
  • (4) 20√2

Some Useful Theorems to Remember:

The Parallelogram:

  • What are the properties of this quadrilateral?

The Rhombus:

  • What are the properties of this quadrilateral?

The Isosceles Trapezoid:

  • What are the properties of this quadrilateral?

The Rectangle:

  • What are the properties of this quadrilateral?

The Square

  • What are the properties of this quadrilateral?

What do you need to show in order to show a quadrilateral is a:

  • Parallelogram?
  • Rectangle?
  • Rhombus?
  • Square?
  • Isosceles Trapezoid?

See also: 

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