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The rough sketch of the quadrilateral ABCD can be drawn as follows.
(1) ∆ABC can be constructed by using the given measurements as follows.
(2) Vertex D is 6 cm away from vertex A. Therefore, while taking A as the centre, draw an arc of radius 6 cm.
(3) Taking C as the centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Joint D to A and C.
ABCD is the required quadrilateral.
(ii) Quadrilateral JUMP JU = 3.5 cm
(1) ∆ JUP can be constructed by using the given measurements as follows.
(2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm, respectively. Let the point of intersection be M.
(3) Join M to P and U.
JUMP is the required quadrilateral.
The rough sketch of the parallelogram MORE can be drawn as follows.
(1) ∆ EOR can be constructed by using the given measurements as follows.
(2) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Therefore, while taking O and E as centres, draw arcs of 4.5 cm radius and 6 cm radius, respectively. These will intersect each other at point M.
(3) Join M to O and E.
MORE is the required parallelogram.
(
1) ∆ BET can be constructed by using the given measurements as follows.
(2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will intersect each other at point S.
(3) Join S to E and T.
(1) ∆ ITL can be constructed by using the given measurements as follows.
(2) Vertex F is 4.5 cm away from vertex L and 3 cm away from vertex I. ∴ while taking L and I as centres, draw arcs of 4.5 cm radius and 3 cm radius, respectively, which will intersect each other at point F.
(3) Join F to T and F to I.
LIFT is the required quadrilateral.
(ii) Quadrilateral GOLD OL = 7.5 cm
(1) ∆ GDL can be constructed by using the given measurements as follows.
(2) Vertex O is 10 cm away from vertex D and 7.5 cm away from vertex L. Therefore, while taking D and L as centres, draw arcs of 10 cm radius and 7.5 cm radius, respectively. These will intersect each other at point O.
(3) Join O to G and L.
GOLD is the required quadrilateral.
(1) Draw a line segment BN of 5.6 cm, and also draw its perpendicular bisector. Let it intersect the line segment BN at point O.
(2) Taking O as the centre, draw arcs of 3.25 cm radius to intersect the perpendicular bisector at points D and E.
(3) Join points D and E to points B and N.
BEND is the required quadrilateral.
(1) Draw a line segment MO of 6 cm and an angle of 105º at point O. As vertex R is 4.5 cm away from the vertex O, cut a line segment OR of 4.5 cm from this ray.
(2) Again, draw an angle of 105º at point R.
(3) Draw an angle of 60º at point M. Let this ray meet the previously drawn ray from R at point E.
MORE is the required quadrilateral.
(ii) Quadrilateral PLAN PL = 4 cm
(1) Draw a line segment PL of 4 cm and draw an angle of 75º at point L. As vertex A is 6.5 cm away from vertex L, cut a line segment LA of 6.5 cm from this ray.
(2) Again, draw an angle of 110º at point A.
(3) Draw an angle of 90º at point P. This ray will meet the previously drawn ray from A at point N.
PLAN is the required quadrilateral.
(1) Draw a line segment HE of 5 cm and an angle of 85º at point E. As vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray.
(2) Vertex R is 6 cm and 5 cm away from vertex H and A, respectively. By taking radii as 6 cm and 5 cm, draw arcs from points H and A, respectively. These will intersect each other at point R.
(3) Join R to H and A.
HEAR is the required quadrilateral.
(1) Draw a line segment OK of 7 cm and an angle of 90º at point K. As vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray.
(2) Vertex Y is 5 cm and 7 cm away from vertex O and A, respectively. By taking
radii as 5 cm and 7 cm, draw arcs from points O and A, respectively. These will intersect each other at point Y.
(3) Join Y to A and O.
OKAY is the required quadrilateral.
(1) Draw a line segment DE of 4 cm and an angle of 60º at point E. As vertex A is 5 cm away from vertex E, cut a line segment EA of 5 cm from this ray.
(2) Again, draw an angle of 90º at point A. As vertex R is 4.5 cm away from vertex A, cut a line segment RA of 4.5 cm from this ray.
(3) Join D to R.
DEAR is the required quadrilateral.
(1) Draw a line segment RU of 3 cm and an angle of 120º at point U. As vertex E is 4 cm away from vertex U, cut a line segment UE of 4 cm from this ray.
(2) Next, draw an angle of 75º at point R. As vertex T is 3.5 cm away from vertex R, cut a line segment RT of 3.5 cm from this ray.
(3) Join T to E.
TRUE is the required quadrilateral.
Rough Figure:
(1) Draw a line segment RE of 5.1 cm and an angle of 90º at points R and E.
(2) As vertex A and D are 5.1 cm away from vertex E and R, respectively, cut line segments EA and RD, each of 5.1 cm from these rays.
(3) Join D to A.
READ is the required square.
Rough Figure:
(1) Draw a line segment AC of 5.2 cm and draw its perpendicular bisector. Let it intersect the line segment AC at point O.
(2) Draw arcs of 6.4/2 = 3.2 on both sides of this perpendicular bisector. Let the arcs intersect the perpendicular bisector at points B and D.
(3) Join points B and D with points A and C.
ABCD is the required rhombus.
(1) Draw a line segment AB of 5 cm and an angle of 90º at points A and B.
(2) As vertex C and D are 4 cm away from vertex B and A, respectively, cut line segments AD and BC, each of 4 cm, from these rays.
(3) Join D to C.
ABCD is the required rectangle.
(1) Draw a line segment OK of 5.5 cm and a ray at point K at a convenient angle.
(2) Draw a ray at point O parallel to the ray at K. As the vertices A and Y are 4.2 cm away from the vertices K and O, respectively, cut line segments KA and OY, each of 4.2 cm, from these rays.
(3) Join Y to A.
OKAY is the required rectangle.
