Activities

1. True or false.  A square is a quadrilateral.
   
   
2. A __________ is a quadrilateral.
   
   
3. True or false.  A rectangle has opposite sides parallel.
   
   
4. What two shapes have four right angles?
   
   
5. A trapezoid is a ____________
   
   
   1. Square
   2. Rectangle
   3. Parallelogram
   4. Quadrilateral

6. What is one difference between a square and a rectangle?
   
   
7. List two properties that a rhombus and a square have in common.
   
   
8. Is a trapezoid also a parallelogram?
   
   
9. Can a rhombus be classified a parallelogram?  Why?
   
   
   1. Yes, because all interior angles add up to 360 degrees
   2. Yes, because all properties of a parallelogram are also properties of a rhombus
   3. No, because all four sides of a parallelogram are not congruent
   4. No, because all properties of a rhombus are not properties of a parallelogram
      
      
10. Is a parallelogram always a quadrilateral?
    
    
11. A quadrilateral is not always a square.  Why not?
    
    
12. What do all of the following have in common:   rectangle, parallelogram, quadrilateral?
    
    
13. List two identical features of a rectangle and a parallelogram.
    
    
14. List one feature of a rhombus that a parallelogram does not possess.
    
    
15. What two properties do a rhombus and a rectangle have in common?
    
    
    1. All sides are congruent, opposite sides are parallel
    2. Opposite sides are congruent, opposite sides are parallel
    3. Opposite angles are congruent, all sides are congruent
    4. All angles are congruent, opposite sides are congruent

16. Is a parallelogram always a square?  Why?  Why not?
    
    
17. Why is a square considered to be a quadrilateral, but a quadrilateral is not necessarily a square?
    
    
18. When the four points are connected in the order (1, 1) to (3, 1) to (5, 5) to (3, 5), explain why the plotted shape on the coordinate grid is not a rhombus.

19. Explain how to change the plotted points on the grid so a rectangle is formed.  Justify your moves.

20. Which statement(s) are false?  Why?
    
    
    1. A right triangle is a form of a polygon
    2. Pentagons are a specific type of parallelogram
    3. All squares are quadrilaterals and parallelograms and rectangles.
       
       
21. Four sides of a quadrilateral are congruent and parallel.  Explain why this statement is true or false.
    
    
22. Which statement incorrectly compares a rectangle and a quadrilateral?  Explain why.
    
    
    1. Both shapes are polygons
    2. Both shapes are also parallelograms
    3. Both shapes have four angles
       
       
23. A rectangle is a polygon.  List two other classifications for a rectangle and explain why.

Answer Key/Rubric

1. True
   
   
2. Student lists any four sided polygon (square, rhombus, rectangle, parallelogram, trapezoid)
   
   
3. True
   
   
4. Square, rectangle
   
   
5. d

6. Square has 4 congruent sides, a rectangle has only opposite sides congruent.
   
   
7. Answers will vary.  Ex:  All sides are congruent.  Opposite sides are parallel. 
   
   
8. No
   
   
9. b
   
   
10. Yes
    
    
11. Answers will vary.  Example:  A square has four 90 degree angles which is not a requirement for a quadrilateral.
    
    
12. Answers will vary.  Examples:  4-sided figures, sum of the interior angles are 360 degrees.
    
    
13. Answers will vary.  Examples:  Opposite sides are equal, opposite sides are parallel, opposite angles are congruent, 4-sided figures, sum of the interior angles are 360 degrees
    
    
14.  All sides congruent
    
    
15. b

16. No.  Answers will vary.  A parallelogram is defined by opposite sides parallel and congruent.  A square has opposite sides parallel and congruent but must also have all four sides congruent.  Therefore, a parallelogram is not always a square.
    
    
17. Answers will vary.  A quadrilateral is defined as a four sided figure, which is what a square is.  However, a square has additional properties a quadrilateral does not, such as all sides are congruent and four right angles. It is the lack of these properties that do not allow the quadrilateral to always be considered a square.
    
    
18. Answers will vary. A rhombus has four congruent sides.  The sides of this shape are not congruent, only opposite sides are congruent.  The length of the shorter side is two (counted the blocks) and the length of the longer sides is much larger than two.
    
    
19. Answers will vary.  If the point located at (1, 6) is moved to (1, 2) [or (6, 2) is moved to (6, 6)] a rectangle is formed.  The new shape is a rectangle because opposite sides are congruent and parallel and now contain four right angles.  The shorter side is 2 and the longer side is 5 (counted blocks).  There are four right angles because the sides of the rectangle are horizontal and vertical segments with endpoints on the grid.  By definition, the coordinate grid has vertical and horizontal segments intersecting at 90 degree angles.
    
    
20. Statement B.  Explanations will vary.  A parallelogram is a four-sided figure and a pentagon is a five-sided figure.
    
    
21. False.  Answers will vary.  Four sided figures can have congruent sides but it is not possible for all four sides to be parallel.
    
    
22. Statement B.  Answers will vary.   Both shapes are not parallelograms, only a rectangle is also a parallelogram (opposite sides parallel and congruent).   A quadrilateral is just a four sided figure and does not have to be a parallelogram.
    
    
23. A rectangle is a quadrilateral because it has four sides.  A rectangle is a parallelogram because it has opposite sides congruent and parallel.