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CONSTRUCTING A QUADRILATERAL WE SHALL LEARN HOW TO CONSTRUCT A UNIQUE QUADRILATERAL BY FOLLOWING METHODS : When four sides and one diagonal are given. When two diagonals and three sides are given. When two adjacent sides and three angles are given. When three sides and two included angles are given. When other special properties are known. CONSTRUCTING A QUADRILATERAL WHEN FOUR SIDES AND ONE DIAGONAL ARE GIVEN Example : Construct a quadrilateral PQRS where PQ = 4cm, QR = 6cm, RS= 5cm, PS = 5.5cm and PR = 7cm 7 cm Step 1 :Construct a triangle PQR using SSS criterion. 7 cm STEP 2 :WITH P AS CENTRE DRAW AN ARC OF RADIUS 5.5 CM . 7 cm STEP 3 :NOW, WITH R AS CENTRE DRAW AN ARC OF RADIUS 5 CM INTERSECTING ANOTHER ARC AT POINT S 7 cm STEP 4 :NOW JOIN PS AND RS. 7 cm PQRS is the required quadrilateral. CONSTRUCTING A QUADRILATERAL WHEN TWO DIAGONALS AND THREE SIDES ARE GIVEN. D 7 cm B 5.5cm Example : Construct a quadrilateral ABCD, given that BC =4.5 cm, AD = 5.5 cm, CD = 5 cm, AC = 5.5 cm and diagonal BD = 7 cm. C A STEP 1 :DRAW TRIANGLE ACD USING SSS CRITERION D A 5.5 cm C STEP 2 :WITH D AS CENTRE DRAW AN ARC OF RADIUS 7 CM. D A 5.5 cm C STEP 3 :NOW, WITH C AS CENTRE DRAW AN ARC OF RADIUS 4.5 CM INTERSECTING ANOTHER ARC AT POINT B. D A 5.5 cm B C STEP 4 :JOIN AB, DB AND CB D 7 cm A 5.5 cm B C ABCD is required triangle CONSTRUCTING A QUADRILATERAL WHEN TWO ADJACENT SIDES AND THREE ANGLES ARE KNOWN M Example : Construct a quadrilate ral MIST where MI 3.5 cm, IS 6.5 cm, M 75 , I 105 and S 120 120 T I 105 75 S Step 1 : Draw a line MI 3.5 cm and make an MIX 105 . X 105 M 3.5 cm I Step 2 : Measure IX 6 . 5 and name that point S. Now make ISY 120 . Y X 120 105 M 3.5 cm I S Step 3 : Now make IMZ 75 Z Y X 120 75 M 3.5 cm 105 I S STEP 4 :MARK THAT POINT T WHERE SY AND MZ MEET. Z Y T X 120 75 M 3.5 cm 105 I S MIST is the required Quadrilateral. CONSTRUCTING A QUADRILATERAL WHEN THREE SIDES AND TWO INCLUDED DIAGONALS ARE GIVEN. Example : - Construct a D Quadrilate C ral ABCD, where AB 4 cm, Bc 5 cm, CD 6.5 cm, B 105 and C 80 . A 4 cm B Step 1 : Draw a line BC 5 cm and Draw an of 105 along BX. X 105 B 5 cm C Step 2 : Measure BX 4 cm and name that point A. X A 105 B 5 cm C Step 3 : Now make BCY 80 Y X 105 B 5 cm 80 C Step 4 : Now, with C as centre, Draw an arc of length 6.5 cm that cuts CY at point D. Y D X 105 B 5 cm 80 C Step5 : Join AD Y X D 105 B 5 cm ABCD is the required Quadrilateral. 80 C CONSTRUCTING A QUADRILATERAL WHEN OTHER SPECIAL PROPERTIES ARE KNOWN. Some examples are :1. Draw a square of side 5 cm. 2. Construct a rhombus ABCD where AC = 6 cm, and BD = 7 cm. EXAMPLE 1 :DRAW AN SQUARE ABCD OF Initially 5 it appears that 4.5 cm SIDE CM. D only one measurements 90 90 4.5 cm 4.5 cm has been given. Actually we have many more details with us, because the figure is special quadrilateral namely a square. We know that each of its angles is a Right angle. C 90 A 90 4.5 cm B Rhombus are Perpendicular bisectors of one another. So, first we draw AC = 7 cm and construct its perpendicular bisector. Let them meet at O. cut off 3 cm lengths on either side of the drawn bisector . You get now B and D. A 6 cm XAMPLE 2 :CONSTRUCT A RHOMBUS ABCD WHERE AC = of6 CM, AND BD = 7D CM. As we know the diagonals O 7 cm B C