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6

Q1. Construct a rhombus ABCD, where diagonal AC = 4.3 cm and diagonal BD = 3.4 cm.

Solution

space space Steps space of space construction colon space space
left parenthesis 1 right parenthesis space space space space Draw space AC space equals space 4.3 space cm
left parenthesis 2 right parenthesis space space space space Draw space perpendicular space bisector space to space AC space which space cuts space AC space at space straight O. space space
left parenthesis 3 right parenthesis space space space space From space this space perpendicular space cut space OD space and space OB space such space that comma
space space space space space space space space space OD equals OB equals 1 half BD equals 1 half cross times 3.4 equals 1.7 space cm
left parenthesis 4 right parenthesis space space space space Join space AB comma space BC comma space CD space and space DA. space space
Hence comma space ABCD space is space the space required space rhombus.
Q2. Draw any rectangle ABCD.

Solution

1. Draw a segment AB of any length. 2. Using a protractor, draw a ray AP perpendicular to segment AB at point A. Using the protractor, draw a ray BQ perpendicular to segment AB at point B. 3. Taking a radius less than segment AB and placing the compass point on point A, draw an arc to cut ray AP at D. Without changing the radius, and placing the compass point on point B, draw an arc to cut ray BQ at C. Draw segment DC. Thus we get rectangle, ABCD.  
Q3. Draw any square ABCD.

Solution

1. Draw a segment AB of any length. 2. Using a protractor, draw a ray AP perpendicular to segment AB at point A. Using the protractor, draw a ray BQ perpendicular to segment AB at point B. 3. Placing the point of the compass on point A and taking a radius equal to AB, draw an arc to cut AP at D. Taking the same radius and placing the compass point on point B, draw an arc to cut ray BQ at C. Draw DC. Thus we get a square ABCD.
Q4. Draw a rectangle ABCD such that AB = 5.5 cm and BC = 3.5 cm. 

Solution

Steps space of space construction colon space space
left parenthesis 1 right parenthesis space space space Draw space segment space AB space equals space 5.5 space cm
left parenthesis 2 right parenthesis space space space Using space straight a space protractor comma space draw space straight a space ray space AX space perpendicular space AB space at space Point space straight A space and space
space space space space space space space space space straight a space ray space BY space perpendicular space AB space at space Point space straight B. space
left parenthesis 3 right parenthesis space space space Placing space the space point space of space compass space on space point space straight A space and space taking space straight a space radius space of space 3.5 space cm comma space
space space space space space space space space space draw space an space arc space of space circle space to space cut space AX space at space point space straight D. space
space space space space space space space space space Taking space the space same space space radius space and space placing space the space point space of space compass space on space point space straight B comma space
space space space space space space space space space draw space an space arc space of space circle space to space cut space BY space at space point space straight C. space
left parenthesis 4 right parenthesis space space space Draw space segment space CD. space space
Thus comma space straight a space rectangle space ABCD space with space AB space equals space 5.5 space cm space and space BC space equals space 3.5 space cm space is space constructed.
Q5. Draw square MNOP having a side of 5.8 cm.

Solution

Steps space of space construction colon
left parenthesis 1 right parenthesis space space space space Draw space segment space MN space equals space 5.8 space cm.
left parenthesis 2 right parenthesis space space space space Using space straight a space protractor comma space draw space straight a space ray space MX space perpendicular space MN space at space point space straight M.
left parenthesis 3 right parenthesis space space space space Using space straight a space protractor comma space draw space straight a space ray space NY space perpendicular space MN space at space point space straight N.
left parenthesis 4 right parenthesis space space space space Taking space straight M space as space centre space and space radius space equal space to space MN comma space draw space an space arc space to space cut
space space space space space space space space space space ray space MX space at space straight P.
left parenthesis 5 right parenthesis space space space space Taking space straight N space as space centre space and space same space radius comma space draw space an space arc space to space cut space ray space NY space at space straight O.
left parenthesis 6 right parenthesis space space space space space Draw space OP.
Hence comma space MNOP space is space the space required space square.
Q6. Construct a parallelogram PQRS, where PQ = 3.5 cm, QR = 4.0 cm and PR = 6.5 cm.

Solution

Steps space of space construction colon space space space space space
left parenthesis 1 right parenthesis space space space space space PR space is space one space of space the space diagonal space of space parallelogram space PQRS space and space
space space space space space space space space space space PQ space is space the space base. space Hence comma space draw space PQ space equals space 3.5 space cm. space
left parenthesis 2 right parenthesis space space space space space Taking space straight P space as space center comma space draw space an space arc space of space radius space 6.5 space cm. space
left parenthesis 3 right parenthesis space space space space space Taking space straight Q space as space center comma space draw space an space arc space of space radius space 4 space cm space to space intersect space the space
space space space space space space space space space space space previous space arc space at space straight R. space Draw space seg space PR space and space QR. space
left parenthesis 4 right parenthesis space space space space space space straight l left parenthesis PS right parenthesis space equals space straight l left parenthesis QR right parenthesis space equals space 4 space cm space and space straight l left parenthesis PQ right parenthesis space equals space straight l left parenthesis SR right parenthesis space equals space 3.5 space cm. space
space space space space space space space space space space space Taking space straight P space as space center comma space draw space an space arc space of space radius space 4 space cm space and space
space space space space space space space space space space space space taking space straight R space as space center comma space draw space an space arc space of space radius space 3.5 space cm space to space intersect space the space
space space space space space space space space space space space space previous space arc space at space straight S. space
space space space space space space space space space space space space Draw space seg space PS space and space RS. space
Hence comma space parallelogram space PQRS space space has space been space constructed space with space given space measurements.
Q7. Construct a rhombus ABCD, whose one side and one diagonal 4 cm and 5 cm respectively.

Solution

Steps space of space construction colon space space
left parenthesis 1 right parenthesis space space space space Draw space AC space equals space 5 space cm space which space is space one space of space the space diagonal space of space rhombus space ABCD. space
left parenthesis 2 right parenthesis space space space The space four space sides space of space straight a space rhombus space are space congruent. space space
space space space space space space space space space space One space side space of space straight a space rhombus space equals space 4 space cm. space
space space space space space space space space space space Hence comma space all space the space sides space of space the space given space rhombus space equals space 4 space cm. space
left parenthesis 3 right parenthesis space space space space Now comma space taking space straight A space as space the space center comma space draw space arcs space of space radius space 4 space cm space above space and space
space space space space space space space space space space below space the space seg space AC. space space
left parenthesis 4 right parenthesis space space space space Similarly comma space taking space straight C space as space the space center comma space draw space arcs space of space radius space 4 space cm space above space
space space space space space space space space space space and space below space the space seg space AC. space
left parenthesis 5 right parenthesis space space space space The space point space of space intersection space of space the space arcs space above space the space seg space AC space is space the space vertex space straight D
space space space space space space space space space space and space the space point space of space intersection space of space the space arcs space below space the space seg space AC space is space the space vertex space straight B. space
Hence comma space rhombus space ABCD space has space been space constructed space with space the space given space measurements.
Q8. Construct a rhombus LMNO, where LN = 3 cm and MO = 5 cm.

Solution

Steps space of space construction colon
left parenthesis 1 right parenthesis space space space Draw space diagonal space LN space equals space 3 space cm.
left parenthesis 2 right parenthesis space space space Construct space the space perpendicular space bisector space of space LN space to space get space the space mid minus point space straight P.
left parenthesis 3 right parenthesis space space space With space straight P space as space centre space and space half space of space MO comma space straight i. straight e. space 2.5 space cm space as space radius comma space draw space an space arc space above space and space below space
space space space space space space space space to space cut space the space perpendicular space bisector space at space straight O space and space straight M space respectively.
left parenthesis 4 right parenthesis space space space Join space LO comma space ON comma space MN comma space LM space to space get space the space rhombus space LMNO.
Q9. Draw quadrilateral DEFG, where nbsp;DE = 5 cm, EF = 6.5 cm, FG = 7 cm, DG = 3 cm, DF = 8 cm.

Solution

Steps space of space construction colon space space
left parenthesis 1 right parenthesis space space space space space space Draw space DF space equals space 8 space cm comma space which space is space the space diagonal space of space square DEFG. space
left parenthesis 2 right parenthesis space space space space space Taking space straight D space as space centre comma space draw space an space arc space of space radius space 3 space cm. space
space space space space space space space space space space space Taking space straight F space as space centre comma space draw space an space arc space of space radius space 7 space cm. space
space space space space space space space space space space space straight G space will space be space their space point space of space intersection. space
space space space space space space space space space space space Draw space seg space DG space and space FG. space
left parenthesis 3 right parenthesis space space space space space Similarly comma space taking space straight D space as space centre comma space draw space an space arc space of space radius space 5 space cm space and space
space space space space space space space space space space space taking space straight F space as space centre comma space draw space an space arc space of space radius space 6.5 space cm. space space
space space space space space space space space space space space straight E space will space be space their space point space of space intersection. space
space space space space space space space space space space space Draw space seg space DE space and space FE. space
Hence comma space square DEFG space has space been space constructed space with space the space given space measurements.
Q10. Construct a rhombus having one side = 4.0 cm and one diagonal = 5.2 cm.

Solution

Steps space of space construction colon space
left parenthesis 1 right parenthesis space space space space Draw space segment space AB space equals space 4 space cm
left parenthesis 2 right parenthesis space space space space With space straight A space as space centre space and space radius space 5.2 space cm comma space and space straight B space as space centre space and space radius space 4 space cm comma space
space space space space space space space space space draw space arcs space which space intersect space each space other space at space straight C. space
left parenthesis 3 right parenthesis space space space space Join space AC space and space BC. space
left parenthesis 4 right parenthesis space space space space Again space with space centre space straight A space and space straight C space and space radius space 4 space cm comma space draw space arcs space which space intersect space
space space space space space space space space space each space other space at space straight D space
left parenthesis 5 right parenthesis space space space space Join space AD space and space CD. space space Join space BD.
Hence comma space ABCD space is space the space required space rhombus. space


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