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Mathematics Teachers Association of the Philippines
                      Self Learning Kit : Grade 7 – Geometry

                          Quadrilaterals


Objectives      Credits       Review                Discussion               Activities   Web Links


                                Click the icons to navigate.


                             Prepared by: Mr. Alvin Patrick Q. Peñaflorida
                               VALENZUELA NATIONAL HIGH SCHOOL
                                 Division of City Schools - VALENZUELA
Objectives
Illustrate, name and identify
     the different kinds of
         quadrilaterals


                    Back Home   Next
Credits
Reference Books:
1. E-Math III by Oronce and Mendoza, First Edition, 2007
2. The University of Chicago School Mathematics Project
(GEOMETRY) by Usiskin et. al., second Edition, 1997

Web:
1.   http://www.mathsisfun.com
2.   http://www.mathopenref.com
3.   http://www.animatedgif.net
4.   http://www.gifs-paradise.com
5.   http://classroomclipart.com


                                             Back Home     Next
Review
Click here to
begin

                Back Home   Next
Which of the following figure is a polygon ?



                   Click the figure that you think is a polygon.




                                 Points
Click here for hint!!!
                                   III
Click here if you got 3 points                        Back Home    Next
Very Good!
This is a polygon since:

a. It is a closed plane figure formed by
three or more line segments;
 b. each segments intersects exactly two
        others, one at each endpoint;
 c. and no two segments with a common
        endpoint are collinear.

                                  Back Home   Next
Nice try…
But this is not a polygon may be
because:
a. It is NOT a closed plane figure formed
by three or more line segments;
b. each segments DO NOT intersects
    exactly two others, one at each
    endpoint;
c. or THERE ARE two segments with a
    common endpoint that are collinear.

                                   Back Home   Next
Definition of POLYGON
A   Polygon:
a. is a closed plane figure formed by three
or more line segments;
b. each segments intersects exactly two
   others ,one at each endpoint;
c. and no two segments with a common
   endpoint are collinear.


                               Back Home   Next
QUADRILATERALS
      “Four Sided Polygon”
                                       Discussion
The figure below shows
coplanar points A,B,C
and D such that no three
points are collinear.
                         B
    A

                             C
             D
                             Back   Home   Next
QUADRILATERALS
The four points A,B,C
and D are the vertices,
which joined by four
segments.
             B
     A

                 C
         D
                 Back   Home   Next
QUADRILATERALS
The union of these four
segments is called
QUADRILATERAL.

              B
     A

                   C
         D
                  Back   Home   Next
NAMING
   QUADRILATERALS
The given QUADRILATERAL
can be named by listing its                         B
vertices starting with any vertex A
and writing or reading the other
vertices in either CLOCKWISE
or COUNTERCLOCKWISE                                        C
direction                               D

 Click here            Click here
 for
 CLOCKWISE             for
                     COUNTERCLOCKWISE
      ABCD                  ADCB


                                      Back   Home   Next
NAMING
                  QUADRILATERALS

Hence, the quadrilateral below can be named as:
                                                      B
 CLOCKWISE       COUNTERCLOCKWISE   A
     ABCD                 ADCB
     BCDA                 DCBA                               C
     CDAB                 CBAD            D
     DABC                 BADC




                                        Back   Home   Next
“Hierarchy of Quadrilaterals”

                   Trapezium

                                       Trapezoid
        Kite



                   Parallelogram
                                               Isosceles
                                               Trapezoid
Back
         Rhombus                   Rectangle

Home                    Square



Next       Parallelogra
           Rectangle
           Trapezoi
       Isosceles
           Rhombus
           Trapeziu
             Square
              Kite
Trapezium
         T

                              A
M

MTAP                P


    A Quadrilateral with
      no parallel sides.


                     Back   Home   Next
A            M                MATH
Trapezoid

                   T                       H

A quadrilateral that has exactly one
pair of opposite sides parallel.
             The sides that are parallel are called
             "bases". The other sides are "legs".


                                    Back       Home   Next
R
                        CARE
      Kite
                              E                       A
A quadrilateral that:
 * has two pairs of sides.
 * each pair is adjacent sides
 (they meet) that are equal in        C
 length. 
Also, the angles are equal where the pairs meet. 
Diagonals (dashed lines) meet at a right angle, and
one of the diagonal bisects (cuts equally in half) the
other.
                                    Back       Home   Next
C                        E

    Parallelogram
                            I                     N
                                    NICE

A quadrilateral where opposite
sides are parallel.
   Also:
   * opposite sides are equal in length,
   *and opposite angles are equal


                                    Back   Home   Next
IsoscelesTrapezoid
                 O              L


             V                      E
                      LOVE
A quadrilateral which has a pair of opposite
sides parallel.
Also:

*the sides that aren't parallel are equal in
length
*and both angles coming from a parallel side
          are equal
                                Back    Home   Next
Rhombus
                        T

           E                             R
                                             TRUE
                        U

A quadrilateral where all sides have equal length.
Also :
*opposite sides are parallel 
*opposite angles are equal
*and the diagonals of a rhombus bisect each other
at right angles
                                  Back   Home   Next
Rectangle
              L                     E



               I                    F
                          LIFE

A quadrilateral where every angle is a right
angle (90°).
Also:
* opposite sides are parallel 
* and opposite sides have equal length.
                                  Back   Home   Next
F                    A

  Square
                        R                    I
                                 FAIR

A quadrilateral where all sides have equal length.

Also:
*every angle is a right angle (90°)
*and opposite sides are parallel.
                                      Back   Home   Next
The Hierarchy of Quadrilaterals
        In the hierarchy of quadrilaterals shown in the
above figures, a quadrilateral below another on the family
tree is a special case of the one above it. A rectangle, for
example, is a special case of a parallelogram. Thus, you
can say that a rectangle is a parallelogram but not that a
parallelogram is a rectangle (a parallelogram is only
sometimes a rectangle).
L                          E            C                  E



I                          F      I                   N
           LIFE                              NICE

                    Back   Home       Next
Click all Quadrilaterals
              in the set below.
                                                Activities

                Very Good!
      You’ve got all of the QUADRILATERALS
                    in the set!!!
      Click here if you got 4 correct answer…

                   Correct!
Correct!                                 Correct!

                   Correct!


                 Back Home    Next
Practice!
 Which of the following label is a        P                          R
 possible name for the
 quadrilateral on the right?
Choose your answer by clicking
the letter of your choice.
                                      Y                         A
  A           RYAP Sorry! Click here for HELP

  B          PRAY        Very Good!

  C          AYRP Sorry! Click here for HELP

  D          APRY Sorry! Click here for HELP
                                                Back   Home   Next
Practice makes PERFECT!
 Which of the following label is             V
 NOT a possible name for the                                 O
 quadrilateral on the right?
Choose your answer by clicking
the letter of your choice.
                                                             L
                                             E

A          VLOE        Very Good!

B          LOVE Sorry! Click here for HELP

C          LEVO Sorry! Click here for HELP

D          VELO Sorry! Click here for HELP
                                             Back   Home   Next
One more?
              Which of the following quadrilateral
              below names LIKE?
                    Choose your answer by clicking
                    the letter of your choice.
                        K                      L                 K
       A        L           I
                                        B
                                                 I               E
Back                    E                    Sorry! Click here for HELP
           Sorry! Click here for HELP

                    K                                K             E
Home   C                     I           D            I              L
Next
                  L         E
       Sorry! Click here for HELP                    Very Good!
No Peeking!
            How many Quadrilaterals
            can you find in the following figure?




                   Type your answer here



        9          Click here to check your answer.

Click here for the solution.
                                                      Back   Home   Next
How many Quadrilaterals
can you find in the following figure?




                            Back   Home   Next
How far did you
                  learn?
Tell whether the statement is true or false by clicking your
answer. Good Luck…


All squares are rectangles.

         True                        False


                                             Back   Home
See this one.
Tell whether the statement is true or false by clicking your
answer. Good Luck…


 Some rectangles are squares.

         True                        False


                                             Back   Home
Keep going!
Tell whether the statement is true or false by clicking your
answer. Good Luck…



Some trapezoids are squares.
         True                        False


                                             Back   Home
Your doing great!!!
Tell whether the statement is true or false by clicking your
answer. Good Luck…




All rhombuses are squares.
   True       False


                                             Back   Home
For Greatness and
                 Beyond!!!
 Tell whether the statement is true or false by clicking your
 answer. Good Luck…


Not all squares are rectangles.
          True                        False


                                              Back   Home
Sorry! your answer is wrong…
   Analyze the figure below for
                    L                         E
   help..
         Rectangle


                      I                       F
                                   LIFE
Square           F          A



                 R          I
                     FAIR
                                Back   Home
Sorry! your answer is wrong…
   Analyze the figure below for
                    L                         E
   help..
         Rectangle

                      I                       F
                                   LIFE

Square        F             A



              R             I
                     FAIR
                                Back   Home
Sorry! your answer is wrong…
     Analyze the figure below for
     help..
      Trapezoid
                A          M            MATH




                T                 H
Square      F              A



            R              I
                    FAIR
                               Back   Home
Sorry! your answer is wrong…
   Analyze the figure below for
   help..          T

         E                          R
Rhombus                                    TRUE
                  U
              F                A

Square
              R                I
                      FAIR
                             Back       Home
Sorry! your answer is wrong…
      Analyze the figure below for
      help..         F            A

        Square
                    R                    I
                               FAIR
             L                    E
Rectangle

             I                    F
                        LIFE
                                  Back   Home
Very Good!
 You did a great job…..
A square has four right angles. A rectangle also has
 four right angles. So a square is a rectangle. The
                statement is true.




                                        Home   Next
Very Good!
 You did a great job…..
A square has four right angles. A rectangle also has
 four right angles. So a square is a rectangle. The
                statement is true.




                                        Home   Next
Very Good!
  You did a great job…..
A square has two sets of parallel sides, but a
trapezoid has only one set of parallel sides. The
statement is false.




                                          Home   Next
Very Good!
  You did a great job…..
A rhombus has four congruent sides, but some may
or may not have right angles. The statement is false.




                                          Home   Next
Very Good!
 You did a great job…..
A square has four right angles. A rectangle also has
four right angles. So a square is a rectangle. The
statement
is false.




                                         Home   Next
Web Links
     Click the following interactive links on the
         web for more interesting activities.

http://www.interactivestuff.org/match/maker.phtm

http://teams.lacoe.edu/documentation/classroom




                                            Back Home   Next
Great job pal……
 See you soon…
         Prepared: Mr. Alvin Patrick Q. Peñaflorida
           Division of City Schools - Valenzuela
Home   VALENZUELA NATIONAL HIGH SCHOOL

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Quadrilaterals

  • 1. Mathematics Teachers Association of the Philippines Self Learning Kit : Grade 7 – Geometry Quadrilaterals Objectives Credits Review Discussion Activities Web Links Click the icons to navigate. Prepared by: Mr. Alvin Patrick Q. Peñaflorida VALENZUELA NATIONAL HIGH SCHOOL Division of City Schools - VALENZUELA
  • 2. Objectives Illustrate, name and identify the different kinds of quadrilaterals Back Home Next
  • 3. Credits Reference Books: 1. E-Math III by Oronce and Mendoza, First Edition, 2007 2. The University of Chicago School Mathematics Project (GEOMETRY) by Usiskin et. al., second Edition, 1997 Web: 1. http://www.mathsisfun.com 2. http://www.mathopenref.com 3. http://www.animatedgif.net 4. http://www.gifs-paradise.com 5. http://classroomclipart.com Back Home Next
  • 4. Review Click here to begin Back Home Next
  • 5. Which of the following figure is a polygon ? Click the figure that you think is a polygon. Points Click here for hint!!! III Click here if you got 3 points Back Home Next
  • 6. Very Good! This is a polygon since: a. It is a closed plane figure formed by three or more line segments; b. each segments intersects exactly two others, one at each endpoint; c. and no two segments with a common endpoint are collinear. Back Home Next
  • 7. Nice try… But this is not a polygon may be because: a. It is NOT a closed plane figure formed by three or more line segments; b. each segments DO NOT intersects exactly two others, one at each endpoint; c. or THERE ARE two segments with a common endpoint that are collinear. Back Home Next
  • 8. Definition of POLYGON A Polygon: a. is a closed plane figure formed by three or more line segments; b. each segments intersects exactly two others ,one at each endpoint; c. and no two segments with a common endpoint are collinear. Back Home Next
  • 9. QUADRILATERALS “Four Sided Polygon” Discussion The figure below shows coplanar points A,B,C and D such that no three points are collinear. B A C D Back Home Next
  • 10. QUADRILATERALS The four points A,B,C and D are the vertices, which joined by four segments. B A C D Back Home Next
  • 11. QUADRILATERALS The union of these four segments is called QUADRILATERAL. B A C D Back Home Next
  • 12. NAMING QUADRILATERALS The given QUADRILATERAL can be named by listing its B vertices starting with any vertex A and writing or reading the other vertices in either CLOCKWISE or COUNTERCLOCKWISE C direction D Click here Click here for CLOCKWISE for COUNTERCLOCKWISE ABCD ADCB Back Home Next
  • 13. NAMING QUADRILATERALS Hence, the quadrilateral below can be named as: B CLOCKWISE COUNTERCLOCKWISE A ABCD ADCB BCDA DCBA C CDAB CBAD D DABC BADC Back Home Next
  • 14. “Hierarchy of Quadrilaterals” Trapezium Trapezoid Kite Parallelogram Isosceles Trapezoid Back Rhombus Rectangle Home Square Next Parallelogra Rectangle Trapezoi Isosceles Rhombus Trapeziu Square Kite
  • 15. Trapezium T A M MTAP P A Quadrilateral with no parallel sides. Back Home Next
  • 16. A M MATH Trapezoid T H A quadrilateral that has exactly one pair of opposite sides parallel. The sides that are parallel are called "bases". The other sides are "legs". Back Home Next
  • 17. R CARE Kite E A A quadrilateral that: * has two pairs of sides. * each pair is adjacent sides (they meet) that are equal in C length.  Also, the angles are equal where the pairs meet.  Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other. Back Home Next
  • 18. C E Parallelogram I N NICE A quadrilateral where opposite sides are parallel. Also: * opposite sides are equal in length, *and opposite angles are equal Back Home Next
  • 19. IsoscelesTrapezoid O L V E LOVE A quadrilateral which has a pair of opposite sides parallel. Also: *the sides that aren't parallel are equal in length *and both angles coming from a parallel side are equal Back Home Next
  • 20. Rhombus T E R TRUE U A quadrilateral where all sides have equal length. Also : *opposite sides are parallel  *opposite angles are equal *and the diagonals of a rhombus bisect each other at right angles Back Home Next
  • 21. Rectangle L E I F LIFE A quadrilateral where every angle is a right angle (90°). Also: * opposite sides are parallel  * and opposite sides have equal length. Back Home Next
  • 22. F A Square R I FAIR A quadrilateral where all sides have equal length. Also: *every angle is a right angle (90°) *and opposite sides are parallel. Back Home Next
  • 23. The Hierarchy of Quadrilaterals In the hierarchy of quadrilaterals shown in the above figures, a quadrilateral below another on the family tree is a special case of the one above it. A rectangle, for example, is a special case of a parallelogram. Thus, you can say that a rectangle is a parallelogram but not that a parallelogram is a rectangle (a parallelogram is only sometimes a rectangle). L E C E I F I N LIFE NICE Back Home Next
  • 24. Click all Quadrilaterals in the set below. Activities Very Good! You’ve got all of the QUADRILATERALS in the set!!! Click here if you got 4 correct answer… Correct! Correct! Correct! Correct! Back Home Next
  • 25. Practice! Which of the following label is a P R possible name for the quadrilateral on the right? Choose your answer by clicking the letter of your choice. Y A A RYAP Sorry! Click here for HELP B PRAY Very Good! C AYRP Sorry! Click here for HELP D APRY Sorry! Click here for HELP Back Home Next
  • 26. Practice makes PERFECT! Which of the following label is V NOT a possible name for the O quadrilateral on the right? Choose your answer by clicking the letter of your choice. L E A VLOE Very Good! B LOVE Sorry! Click here for HELP C LEVO Sorry! Click here for HELP D VELO Sorry! Click here for HELP Back Home Next
  • 27. One more? Which of the following quadrilateral below names LIKE? Choose your answer by clicking the letter of your choice. K L K A L I B I E Back E Sorry! Click here for HELP Sorry! Click here for HELP K K E Home C I D I L Next L E Sorry! Click here for HELP Very Good!
  • 28. No Peeking! How many Quadrilaterals can you find in the following figure? Type your answer here 9 Click here to check your answer. Click here for the solution. Back Home Next
  • 29. How many Quadrilaterals can you find in the following figure? Back Home Next
  • 30. How far did you learn? Tell whether the statement is true or false by clicking your answer. Good Luck… All squares are rectangles. True False Back Home
  • 31. See this one. Tell whether the statement is true or false by clicking your answer. Good Luck… Some rectangles are squares. True False Back Home
  • 32. Keep going! Tell whether the statement is true or false by clicking your answer. Good Luck… Some trapezoids are squares. True False Back Home
  • 33. Your doing great!!! Tell whether the statement is true or false by clicking your answer. Good Luck… All rhombuses are squares. True False Back Home
  • 34. For Greatness and Beyond!!! Tell whether the statement is true or false by clicking your answer. Good Luck… Not all squares are rectangles. True False Back Home
  • 35. Sorry! your answer is wrong… Analyze the figure below for L E help.. Rectangle I F LIFE Square F A R I FAIR Back Home
  • 36. Sorry! your answer is wrong… Analyze the figure below for L E help.. Rectangle I F LIFE Square F A R I FAIR Back Home
  • 37. Sorry! your answer is wrong… Analyze the figure below for help.. Trapezoid A M MATH T H Square F A R I FAIR Back Home
  • 38. Sorry! your answer is wrong… Analyze the figure below for help.. T E R Rhombus TRUE U F A Square R I FAIR Back Home
  • 39. Sorry! your answer is wrong… Analyze the figure below for help.. F A Square R I FAIR L E Rectangle I F LIFE Back Home
  • 40. Very Good! You did a great job….. A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is true. Home Next
  • 41. Very Good! You did a great job….. A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is true. Home Next
  • 42. Very Good! You did a great job….. A square has two sets of parallel sides, but a trapezoid has only one set of parallel sides. The statement is false. Home Next
  • 43. Very Good! You did a great job….. A rhombus has four congruent sides, but some may or may not have right angles. The statement is false. Home Next
  • 44. Very Good! You did a great job….. A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is false. Home Next
  • 45. Web Links Click the following interactive links on the web for more interesting activities. http://www.interactivestuff.org/match/maker.phtm http://teams.lacoe.edu/documentation/classroom Back Home Next
  • 46. Great job pal…… See you soon… Prepared: Mr. Alvin Patrick Q. Peñaflorida Division of City Schools - Valenzuela Home VALENZUELA NATIONAL HIGH SCHOOL