"Question 1 Construct the following quadrilaterals. (i) Quadrilateral ABCD AB = 4.5 cm BC = 5.5 cm CD = 4 cm AD = 6 cm AC = 7 cm (ii) Quadrilateral JUMP JU = 3.5 cm UM = 4 cm MP = 5 cm PJ = 4.5 cm PU = 6.5 cm (iii) Parallelogram MORE OR = 6 cm RE = 4.5 cm EO = 7.5 cm (iv) Rhombus BEST BE = 4.5 cm ET = 6 cm
Practical Geometry Page 60"
Answers
To construct a quadrilateral it is necessary to know at least 5 of its parts.
Measurement of 5 parts of a quadrilateral are sufficient to construct it in the following cases:
1. Four sides and one Diagonal.
2. Three sides and both diagonals.
3. Two adjacent sides and 3 angles.
4. Three sides and two included angles.
5. Four sides and one angle.
It is always convenient and helpful to draw a rough sketch of the quadrilateral and indicate the given measurements.
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[ Figure is in the attachment]
Steps of construction:
(a) Draw a line segment AB = 4.5 cm.
(b) Draw an arc of radius 5.5 cm from point B.
(c) Taking radius 7 cm, draw an another arc from point A which intersects the first arc at point C.
(d) Join BC and AC.
(e) Draw an arc of radius 6 cm from point A and draw another arc of radius 4 cm from point C which intersects at D.
(f) Join AD and CD.
It is required quadrilateral ABCD.
ii)
(a) Draw a line segment JU = 3.5 cm.
b) Draw an arc of radius 4.5 cm taking centre J and then draw another arc of radius 6.5 cm taking U as centre. Both the arcs intersect at P.
(c) Join PJ and PU.
(d) Draw arc of radius 5 cm and 4 cm taking P and U as centres which intersect at M.
(e) Join MP and MU.
It is required quadrilateral JUMP.
iii)
(a) Draw a line segment OR = 6 cm.
(b) Draw an arcs of radius 7.5 cm & radius 4.5 cm taking O and R as centres , which intersect at E.
c) Join OE and RE.
(d) Draw an arc of 6 cm radius taking E as centre.
(e) Draw another arc of 4.5 cm radius taking O as centre, which intersects at M.
(f) Join OM and EM.
It is required parallelogram MORE.
iv)
(a) Draw a line segment TE = 6 cm and bisect it into two equal parts.
(b) Draw a perpendicular to TE.
(c) Draw two arcs of 4.5 cm taking E and T as centres, which intersect at S.
(d) Again draw two arcs of 4.5 cm taking E and T as centres, which intersects at B.
(e) Join TS, ES, BT and EB.
It is the required rhombus BEST.
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Hope this will help you....
Step-by-step explanation:
Construction
ANS 1 = Step 1= Draw a line segment AB=4.5cm.
Step 2= Cut an arc of 5.5 cm from C Their point of intersection is B.
Step 3= Cut an arc of 7 cm from C Their point of intersection is A.
Step 4=Cut an arc of 6 cm from D Their point of intersection is A.
Step 5= Cut an arc of 4 cm from D Their point of intersection is C.
Step 5= Join all the points.
ABCD is the required quadrilateral.
ANS 1= Step 1. Draw UM of length 4 cm.
Step 2. Cut an arc of 6.5 cm from U and 5 cm from M. Their point of intersection is P.
Step 3. Cut an arc of 3.5 cm from U and 4.5 cm from P. Their point of intersection is J.
Step 4. Join all the points.
JUMP is the required quadrilateral.
ANS 3= Step 1. Draw OR of length 6cm.
Step 2. Cut an arc of 7.5 cm from O and 4.5 cm from R. Their point of intersection is E.
Step 3. Cut an arc of 4.5 cm from O and 6 cm from E. Their point of intersection is M.
Step 4. Join all the points.
MORE is the required parallelogram.
ANS 4= Step 1. Draw ET of length 6 cm.
Step 2. Draw its perpendicular bisector.
Step 3. Cut an arc of 4.5 cm from E on the perpendicular bisector both above and below ET, the point of intersections are B and S.
Step 4. Join all the points.
BEST is the required rhombus
