Teacher presentation


Kamala Education Society's


Pratibha College Of Education

Student Teachers

Mrs. Sunita Kadam

Mrs. Shilpa Nikam

Dr. Abby Chacko






Unit: Quadrilaterals

Standard: VIII







Objectives of unit

  • Student will be able to recognize different types of quadrilateral, solve problems based on properties of quadrilaterals
  • To make use of/apply the properties of quadrilaterals
  • Thinking Skills Given any quadrilateral student identifies and tell the properties.








Essential Question

  • Define different types of quadrilaterals

Content Questions

  • The opposite sides of a parallelogram are ---------
  • The diagonals of a rhombus --------- --------
  • The --------- of a rectangle are congruent
  • Find the length of diagonal QS of a square PQRS if the length of diagonal PR is 8cm.
  • The diagonals LN and MT of parallelogram LMNT intersect in point O. If l(MO)=5cm, l(LN)=6cm, find l(OT) and l(NO).


    • Definition
        A quadrilateral with all congruent sides and each angle a right angle is called a square.

    • Properties of a square
    • Diagonals
    • of a square are congruent
    • Diagonals of a square bisect each other
    • Diagonals of a square intersect at right angles
    • Each diagonal of a square is the perpendicular bisector of the other


  • Definition
A quadrilateral with each angle a right angle is called a rectangle

  • Properties of a rectangle
  1. The opposite sides of a rectangle are congruent
  2. The diagonals of rectangle are congruent
  3. The diagonals of a rectangle bisect each other


  • Definition
A quadrilateral having all sides congruent is called a rhombus

  • Properties of rhombus
  1. The diagonals of a rhombus bisect each other.
  2. Each diagonal of a rhombus is the perpendicular bisector of the other.
  3. The opposite angles of a rhombus are equal.


  • Definition
A quadrilateral which has opposite sides parallel is called a parallelogram.

  • Properties of a parallelogram
  1. The opposite sides of a parallelogram are congruent.
  2. The opposite angles of a parallelogram are congruent.
  3. The diagonals of a parallelogram bisect each other


  • Definition
    The diagonal that joins the points of intersection of the congruent sides of the kite bisects the other diagonal at right angles.


  • Definition
    The quadrilateral in which only one pair of opposite sides is parallel is called a trapezium.


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    K-W-L Chart


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    Project-Based Learning



    Project-based learning, or PBL (often "PjBL" to avoid confusion with "Problem-based Learning"), is the use of classroom projects, intended to bring about deep learning, where students use technology and inquiry to engage with issues and questions that are relevant to their lives. These classroom projects are used to assess student's subject matter competence compared to traditional testing.

    Project-based learning (PBL): best defined as instruction relating questions and technology relative to the student's everyday lives to classroom projects. Students form their own investigation of their own group which allows students to develop valuable research skills. The students engage in design, problem solving, decision making, and investigative activities. It allows students to work in groups or by themselves and allows them to come up with ideas and realistic solutions or presentations. Students take a problem and apply it to a real life situation with these projects.

    Project-based learning (PBL) provides complex tasks based on challenging questions or problems that involve the students' problem solving, decision making, investigative skills, and reflection that include teacher facilitation, but not direction. Project Based Learning is focused on questions that drive students to encounter the central concepts and principles of a subject hands-on.

    With Project-based learning students learn from these experiences and take them into account and apply them to their lives in the real world. PBL is a different teaching technique that promotes and practices new learning habits. The students have to think in original ways to come up with the solutions to these real world problems. It helps with their creative thinking skills by showing that there are many ways to solve a problem.


    Project-based learning (PjBL): is an approach for classroom activity that emphasizes learning activities that are long-term, interdisciplinary and student-centered. This approach is generally less structured than traditional, teacher-led classroom activities; in a project-based class, students often must organize their own work and manage their own time. Within the project based learning framework students collaborate, working together to make sense of what is going on. Project-based instruction differs from inquiry-based activity by its emphasis on collaborative learning. Additionally, project-based instruction differs from traditional inquiry by its emphasis on students' own artifact construction to represent what is being learned.





    Elements of a good project based learning experience include:

    • A fertile open-ended question or issue that is rich, real and relevant to the students lives
    • Real world use of technology
    • Student-directed learning and/or the deliberate engagement of student voice
    • Collaboration
    • Multi-disciplinary components
    • Long term (more than 3 weeks) time frame
    • Outcomes-based, with an artifact, presentation, or action as a result of the inquiry
    • Project should be focused on making sure students are learning.
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    World of Quadrilaterals


    To the World of Quadrilaterals

    Student presentation


    1. Find the length Of the diagonal QS of a square PQRS if length of diagonal PR is 8 cm.
    • As per given conditions,
    Length of diagonal PR is 8 cm.

    The diagonals of a square are congruent
    . (Property of square.)


    PR =QS.

    But PR = 8 cm…………………..Given

    Therefore QS is also 8 cm .

    • If in the square ABCD , l (AB)=4.5 cm, what are the lengths of the other sides of the squares?
    • As per given conditions,
    AB (side of the square) is 4.5 cm.

    All sides in the square are congruent.


    AB= BC= AC= CD= 4.5 cm.


    The diagonals seg DF and seg EG of the square DEFG intersect each other in point m .If l(DM) =7 cm. find l (EG) ?
    As per given conditions,
    the diagonals of a square intersect each other at M.

    In a square the diagonals bisect each other.

    But , l(DM)=7 cm.
    Therefore,DM=EG=7cm .


    • In rectangle PQRS , l(PQ)=7 cm, l(PS)=9 cm. Find l(QR) and SR.

    In a rectangle the opposite sides are congruent .
    Therefore, PQ=SR AND PS=QR.
    As per given conditions, we can say that

    l(QR)=9 cm and l (SR)=7cm.


    • The diagonals AC and BD of rectangle ABCD intersect each other at point O. If measure angle CAB =25 degrees. find measure angle DAC and CAD.

    In a rectangle the vertex angles are perpendicular to each other.

    Therefore measure angle DAB 90 .
    But , measure angle DAB =m(angle DAC+ angle CAD).
    Therefore, CAD=90-25
                    Therefore CAD=65


    • In quadrilateral LMNP, measure angle L=M=N=P=90.tell what type of quadrilateral LMNP is ? Explain your answer ?

    The following figure is a rectangle as all vertex angles are perpendicular to each other.

    Therefore the quadrilateral is a rectangle .


    • If length of one side of a rhombus is 7.5 cm then find the remaining sides of the rhombus ?

    In a rhombus all sides are congruent.

    Therefore , length of the side is 7.5 cm


    • If measure angle QPS in the rhombus PQRS is 65. Find measure angle QRS ?

    The opposite angles of a rhombus are congruent.

    Angle QPS and QRS are opposite.

    Therefore ,QPS=QRS=65


    • In parallelogram PQRS, measure angle Q=130.find the measure of the other angles of the parallelogram ?

    In a parallelogram the opposite angles are congruent.

    Therefore. Q=S=130

    In a quadrilateral the sum of measures of all angles is 360.

    Therefore ,P+R=360-260
    Therefore , P+R=100

    By 1, we get that P=R=50


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    Diagrams of Quadrilaterals


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    1. Fill in the blanks


    1. The opposite sides of a parallelogram are ---------
    2. The diagonals of a rhombus --------- --------
    3. The --------- of a rectangle are congruent
    4. Find the length of diagonal QS of a square PQRS if the length of diagonal PR is 8cm.

      The diagonals LN and MT of parallelogram LMNT intersect in point O. If l(MO)=5cm, l(LN)=6cm, find l(OT) and l(NO)


    1. Define Quadrilateral


    1. State the different types of quadrilaterals


    1. Define the following terms


    1. Square            2.Rectangle    

    3. Rhombus         4. Parallelogram

    5. Trapezium        6. Kite

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    Discussion Rubric


    Discussion Rubric

    World of Quadrilaterals


    1. Definition of Quadrilateral


    1. Types of Quadrilaterals



    Square                                                    Parallelogram

    Definition                                                    Definition

    Diagrams                                                    Diagram            

    Properties                                                    Properties

    Rectangle                                                    Trapezium        

    Definition                                                    Definition

    Diagrams                                                    Diagram

    Properties                                                    Properties

    Rhombus                                                    Kite

    Definition                                                    Definition

    Diagrams                                                    Diagram

    Properties                                                    Properties




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