Practical Geome...

Construct a rectangle $$ABCD$$, where $$AB=10$$ cm and $$BC=8$$ cm.Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) Join these cuts with a line $$CD$$ and rectangle $$ABCD$$ is formed
2) Draw a straight line $$AB$$ of length $$10$$ cm
3) Draw perpendicular lines at $$A$$ and $$B$$ using protractor.
4) Using compass cut arc at the perpendicular from $$A$$ and $$B$$ of lengths $$8$$ cm

Given are the steps of construction of a quadrilateral ABCD, where AB$$=3.5$$cm, BC$$=6.5$$cm, $$\angle A=75^o$$, $$\angle B=105^o$$ and $$\angle C=120^o$$. Which of the following is a wrong step?
Step I: Draw AB$$=3.5$$cm
Step II: Draw $$\angle$$XAB$$=75^o$$ at A and $$\angle ABY=105^o$$ at B
Step III: With B as centre and radius BC$$=6.5$$cm, draw an arc to intersect BY at C.
Step IV: At C draw $$\angle ADC=120^o$$ such that CZ meets AX at D.

Arrange the following steps in correct order in constructing a square whose one diagonal is $$5$$cm.
Step 1 : Let PQ cut AC at O.
Step 2 : Draw a diagonal AC = $$5$$cm.
Step 3 : Join Ab, BC, CD and DA. Then ABCD is the required square.
Step 4 : Draw PQ the perpendicular bisector of AC.
Step 5 : With O as centre and OA radius draw a circle. Let the circle cut QP at points B and D.

Construct rhombus BEST with following dimensions given-
$$BE=4.5\ cm$$, $$ET=6\ cm$$
Following are the steps given to construct rhombus BEST. Arrange them in correct order-
1) As given quadrilateral is rhombus, opposite sides are equal. Thus, $$BE=ST$$ and $$ES=BT$$. Draw $$\triangle EBT$$ from the given data.
2) Now we have to locate point S. Point S lies on opposite side of point B with reference to ET. Point S is 4.5 cm away from point E. Taking E as centre and radius as 4.5 cm, draw an arc. Point S should lie somewhere on this arc only.
3) Now, point S is 4.5 cm away from point T. Taking T as centre and radius as 4.5 cm, draw an arc. Point S should lie somewhere on this arc also.
4) Point of intersection of both the arcs is point S. Mark point S and complete rhombus BEST.

Construct a quadrilateral ABCD, given that $$BC=4.5\ cm$$, $$AD=5.5\ cm$$, $$CD=5\ cm$$, diagonal $$AC=5.5\ cm$$ and diagonal $$BD=7\ cm$$
Given below are the steps to construct quadrilateral ABCD. Arrange them in correct order.
1) Point B is 7 cm away from point D. By taking D as centre and 7 cm as radius, draw an arc.
2) Point B is 4.5 cm away from point C. By taking C as centre and 4.5 cm as radius, draw another arc.
3) Draw $$\triangle ACD$$ using SSS construction by observing rough figure.
4) Point of intersection of both the arcs is point B. Mark point B and complete quadrilateral ABCD

Construct a quadrilateral PQRS where $$PQ=4\ cm$$, $$QR=6\ cm$$, $$RS=5\ cm$$, $$PS=5.5\ cm$$ and $$PR=7\ cm$$
Following are the steps given to draw $$\Box PQRS$$. Arrange them in correct order-
1) Point S is 5 cm away from point R. So with R as centre, draw an arc of radius 5 cm. (Point S is somewhere on this arc also)
2) From the rough sketch, it is easy to see that $$\triangle PQR$$ can be constructed using SSS construction condition. Draw $$\triangle PQR$$
3) S should lie on both the arcs drawn. So it is the point of intersection of two arcs. Mark S and complete PQRS. PQRS is the required quadrilateral
4) Now we have to locate fourth point S. This point S would lie on the side opposite to Q with reference to PR. For that we have two measurements. S is 5.5 cm away from P. So with P as centre, draw an arc of radius 5.5 cm. (Point S is somewhere on this arc)

Construct parallelogram MORE using given dimensions-
$$OR=6\ cm$$, $$RE=4.5\ cm$$, $$EO=7.5\ cm$$
Following are the steps given to construct parallelogram MORE. Arrange them in correct order-
1) Now we have to locate point R which lies on opposite side of point M with reference to OE. Point R is 6 cm away from point O. Taking point O as centre and radius as 6 cm, draw an arc. (Point R should lie somewhere on this arc)
2) As MORE is parallelogram, $$OR=ME$$ and $$RE=OM$$. From the rough figure, it is clear that $$\triangle OME$$ can be constructed using SSS condition. Draw $$\triangle OME$$
3) Point of intersection of both the arcs is point R. Mark point R and complete parallelogram MORE
4) Now point R is 4.5 cm away from point E. Taking E as centre and 4.5 cm as radius, draw an arc. (Point R should lie somewhere on this arc also)

Construct the quadrilateral ABCD using given data-
$$AB=4.5\ cm$$, $$BC=5.5\ cm$$, $$CD=4\ cm$$, $$AD=6\ cm$$, $$AC=7\ cm$$
Following are the steps given for construction of quadrilateral. Arrange them in correct order-
1) Point D should lie on both the arcs drawn. Thus, point D is point of intersection of two arcs. Mark point D and complete $$\Box ABCD$$
2) Point D is 4 cm away from point C. Thus, by taking C as centre and radius of 4 cm, draw an arc. (Point D should lie on this arc also)
3) Now we have to locate point D. Point D should lie on opposite side of point B with reference to AC. Point D is 6 cm away from point A. Taking A as centre and radius of 6 cm, draw an arc. (Point D should lie somewhere on this arc)
4) By using SSS condition, we can easily draw \triangle ABC. 

Construct a rhombus BEND from the following data-
$$BN=5.6\ cm$$, $$DE=6.5\ cm$$.
Following are the steps given to construct rhombus. Arrange them in correct order-
1) Draw perpendicular bisector of segment BN as diagonals of rhombus are perpendicular bisectors of each other. Let point of intersection be O
2) Draw segment BN of length 5.6 cm.
3) Taking O as centre and radius equal to $$\dfrac { 6.5 }{ 2 } =3.25\ cm$$, draw arcs on both the sides of segment BN to cut perpendicular bisectors in two points E and D.
4) Mark points E and D and complete rhombus BEND

Construct a quadrilateral MIST from the given data.