The document defines quadrilaterals and their properties. It states that a quadrilateral is a polygon with 4 sides and 4 angles, and discusses different types of quadrilaterals. It also explains that the sum of the interior angles of any quadrilateral is always 360 degrees, which is demonstrated through an experiment.

1. K J Somaiya Comprehensive College of Education, Training & Research Name : Monica Panda Roll No : 44 Subject : Mathematics Topic : Quadrilaterals Standard : VII

2. Road Map Objective Definition Introduction Properties Evaluation

3. OBJECTIVE: At the end of the lesson, the students should be able to know the properties of quadrilaterals

4. Definition Polygon – a closed many straight-sided figure. triangle parallelogram octagon heptagon hexagon pentagon

5. Definition Quadrilateral – a polygon with 4 angles and 4 straight sides.

6. Quadrilateral Family parallelogram rectangle rhombus square trapezoid

7. INTRODUCTION WORD QUADRILATERAL IS DERIVED FROM TWO WORDS “ QUADRI ” MEANS “ FOUR ” AND “ LATERAL ” MEANS “ SIDES ”.

8. Quadrilaterals A quadrilateral is a four-sided figure like the one shown. The sides are line segments connected together at their endpoints, called the vertices (plural of vertex ) of the quadrilateral. A quadrilateral is named by its vertices. We call this quadrilateral ABCD or BADC or CDAB etc. (We start with a vertex and then proceed around the quadrilateral, either clockwise or counterclockwise.) A B C D

9. * In quadrilateral ABCD, the vertices are A, B,C, and D * Adjacent vertices are : A and B B and C C and D D and A * Opposite vertices are : A and C B and D A B C D

10. * Adjacent sides -Two sides with common vertex are : AB and BC BC and CD CD and DA DA and AB * Opposite sides are: AB and DC AD and BC A B C D

11. Adjacent angles - Two angles with a common sides are: <A and <D <D and <C <C and <B <B and <A Opposite angles are : <A and <C <B and <D A B C D

12. 4 vertices QUADRILATERALS 4 sides 4 angles QUADRILATERALS A . B . C . D .

13. Segments joining opposite vertices like AC and BD are called diagonals of the quadrilateral. There are 2 diagonals in a quadrilateral . A D C B

14. QUADRILATERALS EXTERIOR OF QUADRILATERAL INTERIOR OF QUADRILATERAL A B C D E . . . . . . G H F J I QUADRILATERAL

15. PROPERTIES OF A QUADRILATERAL

16. IF A LINE CONTAINING ANY ONE OF THE FOUR SEGMENTS PQ, QR, RS, QS IS DRAWN, THEN REMAINING TWO POINTS LIE ON THE SAME SIDE OF THIS LINE. P R Q S

17. The sum of all the angles equals 360º degrees . 70 º 110 º 70 º 110 º 70 º 70 º 110 º 110 º + 360 º

18. QUADRILATERALS EXPERIMENT AIM: To verify that the sum of 4 angles of a quadrilateral is 360 degree. 1. Draw 2 [congruent] quadrilaterals of same shape and size.

19. QUADRILATERALS 2. Draw arcs of same radii at the 4 vertices of the quadrilateral. 3. Colour the region enclosed as shown in the figure.

20. QUADRILATERALS 4. Glue the figure1 in the note book. 5. Separate the angles in figure2 by zig-zag lines as shown.

21. QUADRILATERALS 6. Cut the 4 angles of figure2 as shown.

22. QUADRILATERALS 7. Arrange the angles and paste them side by side. OBSERVATIONS: 4-angles of quadrilateral can be assembled in to a circle. 4-angles of a quadrilateral gives a complete angle. The sum total of the 4 angles of quadrilateral is 360 0.

23. EVALUATION

24. Examples of shapes or curves that are not classified as quadrilaterals. They do not follow the definition of a quadrilateral. Can you give a reason why? Are They Quadrilaterals? A C B

25. Observe the figure and answer the following questions: Name the points in the interior of the quadrilateral PQRS ? 2. Name the points in the exterior of the quadrilateral PQRS ? 3. Name the points on the quadrilateral PQRS ? V W Y X U T . . . . . . R S Q P

26. What is the missing angle? 81 º 58 º 109 º ? A D C B