**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 90^{o }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: **