classification of quadrilaterals grade 9.pptx

Mathematics

1. Classifications of quadrilaterals

2. Learning Targets

3. Answer the question.

4. Types of Quadrilateral Parallelogram Rhombus Rectangle Square Trapezoid Kite

5. It is four- sided polygon. It is named using its consecutive vertices. The symbol □ is used to denote a quadrilaterals. □ BCDA □ ABCD □ DABC □ CDAB □ CBAD □ DCBA □ ADCB □ BADC

6. CONSECUTIVE ANGLES ∠A and ∠B ∠B and ∠C ∠C and ∠D ∠D and ∠A OPPOSITE ANGLES ∠A and ∠C ∠B and ∠D OPPOSITE SIDES         CONSECUTIVE SIDES     DIAGONALS  

7. In the parallelogram ABCD, side AB is parallel to side DC, and side AD is parallel to side BC.  Point E is the midpoint of the two diagonals of the parallelogram. Therefore, length DE = EB, & length AE = EC.   Parallelogram A parallelogram is a quadrilateral with 2 pairs of parallel opposite and equal sides. Similarly, the opposite angles in a parallelogram are equal in measure.

8. Properties of Parallelogram The opposite sides of a parallelogram are parallel. The opposite angles of parallelogram are congruent. The opposite sides of a parallelogram are congruent. The consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. Each diagonal divides a parallelogram into two congruent triangles.  

9. ABCD is a rhombus in which AB is parallel and equal to DC and AD is also parallel and equal to BC. The diagonals AC = BD, and O is the point of intersection of the two diagonals. Rhombus A rhombus is a quadrilateral with all four sides having equal lengths. The Opposite sides of a rhombus are equal and parallel, and the opposite angles are the same.  

10. Properties of Rhombus Properties inherited from the parallelogram. It has four congruent sides. Its diagonals are perpendicular. Each diagonals bisects the angles of the rhombus.

11. Rectangles are very handy to have around. For example, shoe boxes, chopping boards, sheets of paper, picture frames, etc., are rectangular in shape. Rectangles are easy to stack because they have two pairs of parallel sides. Their right angles make sure built things such as houses, office buildings, schools, etc., stand straight and tall.   Rectangle A rectangle is a quadrilateral with 4 right angles (90°). In a rectangle, both the pairs of opposite sides are parallel and equal in length.  

12. Properties of rectangles: All properties of parallelograms. All angles are right angles. The diagonals are congruent.  

13. Real-life examples of squares include computers, keys, coasters, spaces on a chessboard, etc. Square A square is a quadrilateral with 4 right angles (90°). In a square, both pairs of opposite sides are parallel and equal in length. Properties of a square: All properties of parallelograms. All properties of rectangle. All properties of rhombus.  

14. TRAPEZOID

15. ABCD is a trapezium in which side BD is parallel to side CA. The perpendicular line DM is the height (h) of the trapezium, while BD and CA are the bases. Properties of Isosceles Trapezoid Each pair of base angles are congruent. Diagonals are congruent.

16. Properties of a Kite Exactly one pair of opposite angles ( the non- vertex angles ) are congruent. Diagonals are perpendicular. The diagonal through the vertex angles bisects the vertex angles and the other diagonal. Kite A kite is a convex quadrilateral with two distinct pairs of consecutive sides that are congruent.

17. Quadrilateral Angle Sum Theorem

18. The Parallelogram – A Special quadrilateral

19. Learning Targets Identify quadrilaterals that are parallelogram. Illustrate parallelograms that will satisfy the given condition. Appreciate how useful the parallelograms are in creating designs in the different industries

20. Theorem 5.1 The diagonal of a parallelogram divides the parallelogram into two congruent triangles.

21. Theorem 5.2 The opposite sides of a parallelogram are congruent.

22. Theorem 5.3 The opposite angles of a parallelogram are congruent.

23. Theorem 5.4 Consecutives angles of a parallelogram are supplementary.

24. Theorem 5.5 The diagonals of a parallelogram bisect each other.

25. ∠A + ∠B + ∠C + ∠D = 360   ∠A +   ∠A   ∠A +   ∠A =  

26. ∠A + ∠B + ∠C + ∠D = 360   ∠A + 95   ∠A   ∠A +   ∠A =  

27. USING PROPERTIES TO FIND MEASURES OF ANGLES, SIDES AND OTHER QUANTITIES INVOLVING PARALLELOGRAMS 1. A quadrilateral is a parallelogram if opposite sides are congruent and parallel.        

28. EXAMPLE 1. CDEB is a parallelogram. If the measure of CD is 23 and BE is 8x-1, find x. Step 1: Draw the given. C E D B 23 8x-1 Step 2: Identify the opposite sides.     Step 3: Formulate the equation. 23 = 8x – 1   23 + 1 = 8x 24 = 8x x = 3

29. EXAMPLE 2. Find the value of x to make a quadrilateral a parallelogram. Then solve the given sides. C E A R 3x+ 5 6x-10 Step 1: Identify the opposite sides.     Step 2: Formulate the equation. 3x - 6x = – 10 – 5 x = 5   3x + 5 = 6x – 10 - 3x = – 15 Step 3: Find its sides. 3x + 5 =3(5) + 5 =20 6x - 10 = 6(5) - 10 =20

30. 2. A quadrilateral is a parallelogram if: Opposite angles are congruent. Consecutive angles are supplementary.       Consecutive angles       Any pair of consecutive angles are supplementary. The sum of their measures is  

31. EXAMPLE 3. CARE is a parallelogram. If m∠C = 60 find the measures of the other 3 angles. C E A R Step 2: Identify the relationship of each angle to ∠C.     ∠E is consecutive to ∠C Step 1: Draw the given.                   ∠E ≅ ∠A    

32. 3. A quadrilateral is a parallelogram if the diagonals bisect each other.     Diagonal AD bisects BC.   Diagonal BC bisects AD.      

33. EXAMPLE 4. ABCD is a parallelogram. Its diagonal bisects each other at a point E. If AE measures 12 dm, how long is AC and EC?            

34. PT (Logo Making) Logos are excellent examples of how business use geometry, particularly in commercial advertising. Logos allow for easy recall and are readily identifiable with the corporation. Your task is to design a logo using types of quadrilaterals that best describes New Normal . Explain how it describe NEW NORMAL.   Excellent 5 points Good 4 points Fair 3 points Poor 2 points Neatness The design is very neat and clean The design is neat and clean The design contains smudges. The design is messy and sloppy showing no effort to make it neat and clean. Creativity and Originality The logo design is unique and shows a lot of quadrilaterals. The logo design demonstrates some uniqueness and shows a some of quadrilaterals. The logo design is not unique but contains some quadrilaterals. The logo design is not unique and lack of quadrilaterals. Explanation The explanation describes the design detailed and clearly. The explanation describes the design clearly. The explanation describes the design a little difficult to understand. The design is not explain.