Question 13 Marks
Construct a parallelogram $\text{ABCD}$, when:Diagonal $AC = 6.4 \ cm,$ diagonals $BD = 8.2 \ cm$ and angle between the diagonals$ = 60^\circ .$
Answer
Steps:
$1.$ Draw $AC =6.4 cm$.
$2.$ Draw line $BOD$ such that $\angle DOC =60^{\circ}$ and $OB = OD =\frac{1}{2} BD =\frac{1}{2} \times 8.2=4.1 cm$
$3.$ Join $AB, BC, CD$, and $DA$.
$\text{ABCD}$ is the required parallelogram. View full question & answer→Question 23 Marks
Construct a parallelogram $\text{ABCD},$ when$:AB = 4.4 \ cm, AD = 6.2 \ cm$ and $AC = 4.8 \ cm.$
Answer
Steps:
$1.$ Draw $AD=6.2 cm$.
$2.$ Draw $\triangle ACD$.
$3.$ Then draw $\triangle ABC$.
$\text{ABCD}$ is the required parallelogram. View full question & answer→Question 33 Marks
Construct a quadrilateral $\text{ABCD},$ when$:AB = 6.3 \ cm, BC = CD = 4.2 \ cm$ and $\angle ABC = \angle BCD = 90^\circ .$
Answer
Steps :
$1.$ draw $A B=6.3 \ cm$.
$2.$ Draw $B P$ such that $\angle A B P=90^{\circ}$.
$3.$ With $B$ as a center and radii, $4.2 \ cm$ draw an arc $A P$ at $C$.
$4.$ With $C$ as a center draw a line $CD$ with radii $4.2 \ cm$. draw a line such that $\angle BCD=90^{\circ}$.
$5.$ Now join $AD.$
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 43 Marks
Construct a quadrilateral $\text{ABCD},$ when$:AD = AB = 4 \ cm, BC = 2.8 \ cm, CD = 2.5 \ cm$ and $\angle BAD = 45^\circ .$
Answer
Steps:
$1$. Draw $A D=4 \ cm$.
$2.$ Draw $AP$ such that $\angle A=45^{\circ}$.
$3.$ With $A$ as a center with radii, $4 \ cm$ draw an arc at $B$ on $AP.$
$4.$ Now taking B and D as a center and radii $2.8 \ cm$ and $2.8 \ cm$ draw arcs cutting each other at $C$.
$5.$ Now join $BC$ and $C D$.
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 53 Marks
Construct a quadrilateral $\text{ABCD},$ when:$BC = 7.5 \ cm AC = 5.8 \ cm, AD = 3.6 \ cm, CD = 4.2 \ cm$ and $\angle A = 120^\circ .$
Answer
Steps:
$1.$ Draw $AD=3.6 \ cm$
$2.$ draw $AP$ such that $\angle A=120^{\circ}$.
$3.$ With $A$ and $D$ as a center and radii $5.8 \ cm$ and $4.2 \ cm$ draw arcs cutting each other at $C$.
$4.$ Now join $A C$ and $CD$.
$5.$ Now with $C$ as center and radii $7.5 \ cm$ draw an arc at $B$ on $AP.$
$6.$ Now join $CB.$
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 63 Marks
Construct a quadrilateral $\text{ABCD},$ when$:AB = 3.8 \ cm, AC = 4.8 \ cm, AD = 2.8 \ cm, \angle A = 105^\circ $ and $\angle B = 60^\circ .$
Answer
Steps:
$1.$ Draw $A D=2.8 \ cm$
$2.$ Draw $A B=3.8 \ cm$ and $\angle A=105^{\circ}$.
$3.$ Draw $BP$ such that $\angle B=60^{\circ}$.
$4.$ With $A$ as a center and radii $4.8 \ cm$ draw an arc cutting $B P$ at $C$.
$5.$ Join $AC, A D$.
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 73 Marks
Construct a quadrilateral $\text{ABCD},$ when:$\angle A = 90^o, AB = 4.6\ cm, BD = 6.4\ cm, AC = 6.0\ cm$ and $CD = 4.2\ cm.$
Answer
Steps:
$1.$ Draw $AB=4.6\ cm$.
$2.$ Through $A$, draw $AP$ such that Angle $A=90^{\circ}$.
$3.$ With $B$ as a center and radii $6.4 \ cm$ draw an arc at $D$ on $AP.$
$4.$ With $D$ and $A$ as a center and radii, $4.2 \ cm$ and $6 \ cm$ draw an arc cutting each other at $C$.
$5.$ Now join $BD , AC$, and $CB$.
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 83 Marks
Using ruler and compasses only, construct a rectangle each of whose diagonals measure $6\ cm$ and the diagonals interest at an angle of $45^o.$
AnswerTo draw the rectangle follows the steps:
$1.$ First draw a line $AC$ of measure $6\ cm$.
$2.$ Then draw the perpendicular bisector of $AC$ through $O$.
$3.$ At $O$ draw an angle of measure $45^{\circ}$. Then produce $OD$ of measure $3\ cm$ and $OB$ of measure $3\ cm$ each.
$4.$ Now join $AD, AB, BC$, and $CD$ to form the rectangle.
View full question & answer→Question 93 Marks
Using ruler and compasses only, construct a trapezium $\text{ABCD}$, in which the parallel sides $AB$ and $D$ Care $3.3 \ cm$ apart; $AB = 4.5\ cm, \angle A = 120^o BC = 3.6 \ cm$ and $\angle B$ is obtuse.
Answer
Steps:
$1.$ Draw $A B=4.5 \ cm$.
$2.$ now draw $\angle BAS =120^{\circ}$ and draw $EA \perp AB$ such that $AX =3.3 \ cm$.
$3.$Through $X$ draws a line $QR$ which is parallel to $AB$ which cuts $AS$ at $D$.
$4.$ Through $B$ draw an arc taking radius $3.6 \ cm$ at $C$ on $PQ$.
$5.$ Join $CB.$
$\text{ABCD}$ is the required trapezium. View full question & answer→Question 103 Marks
Construct a quadrilateral $ABCD,$ when$:AB = 7.2 \ cm, BC = 5.8 \ cm, CD = 6.3 \ cm, AD = 4.3 \ cm$ and $\angle A = 75^\circ .$
Answer
Steps:
$1.$ Draw $AB =7.2 \ cm$
$2.$ Through A draw AP such that $\angle A=75^{\circ}$.
$3. $From $A P$ cut $A D=4.3 \ cm$
$4.$ With $D$ and $B$ as center and radii $6.2 \ cm$ and $5.8 \ cm$ respectively, draw arcs cutting each other at $C$.
$5.$ Join $DC$ and $BC$.
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 113 Marks
Construct a rhombus $\text{ABCD},$ when:Diagonal $AC = 6.3 \ cm$ and diagonal $BD = 5.8 \ cm.$
Answer
Steps:
$1.$ Draw $AC =6.3 \ cm$.
$2.$ Draw perpendicular bisector to $AC$ which cuts $AC$ at $O$.
$3.$ From this perpendicular cut $OD$ and $O$B such that,
$OD = OB =\frac{1}{2} BD =\frac{1}{2} \times 5.8=2.9 \ cm$.
$4.$ Join $AB , BC , CD$, and $DA$.
$\text{ABCD}$ is the required rhombus. View full question & answer→Question 123 Marks
Construct a rhombus $\text{ABCD}$, when:Its one side $= 6 \ cm$ and $\angle A = 60^o.$
Answer
Steps:
$1.$ Draw a line $A B=6 \ cm$.
$2.$ At $A$, we construct $\angle BAP=60^{\circ}$.
$3.$ From $A P$, we cut at $D$ taking $A D=6 \ cm$.
$4.$ Through $B$, we draw $BQ \| AD$.
$5.$ Through $D$, we draw $DC \| A B$ to cut $BQ$ at $C$.
$\text{ABCD}$ is the required rhombus. View full question & answer→Question 133 Marks
Construct a trapezium $\text{ABCD}$, when$:AB =4.8 cm, BC =6.8 cm, CD =5.4 cm, \angle B =60^{\circ}$ and $AD \| BC$.
Answer
Steps:
$1.$ Draw $BC =6.8 \ cm$.
$2.$ With $B$ as a center and radii $4.8 \ cm$ draw an arc at $A$ such that $\angle B =60^{\circ}$.
$3.$ From point draw a line AP such that $AP \| BC$.
$4.$ With $C$ as a center and radii $5.4 \ cm$ draw an arc at $D$ on the line $AP$.
$5.$ Now join $AB, CD$.
$\text{ABCD}$ is the required trapezium. View full question & answer→Question 143 Marks
Construct a quadrilateral $\text{ABCD},$ when$:AB = 3.2 \ cm, BC = 5.2 \ cm, CD = 6.2 \ cm, DA = 4.2 \ cm$ and $BD = 5.2 \ cm.$
Answer
Steps:
$1.$ Draw $AB=3.2 \ cm$.
$2.$ With $A$ as a centre draw an arc at $D$ and with $B$ as a centre and radius $5.2 \ cm$ draw an arc at $D.$
$3.$ Join $AD$ and $DB.$
$4.$ With $D$ and $B$ as a centre taking radius $6.2 \ cm$ and $5.2 \ cm$ draw an arc at $C$. Now join $BC$ and $DC$.
$\text{ABCD}$ is the required quadrilateral. View full question & answer→Question 153 Marks
Construct a rectangle $\text{ABCD}$, when:
One diagonal $= 6.0 \ cm$ and the acute angle between the diagonals $= 45^o.$
Answer
Steps:
$1.$ Draw $AC=6 cm$.
$2.$ Draw the right $\triangle ACB$.
$3.$ Draw the right $\triangle ADB$.
$4.$ Join $DC.$
$\text{ABCD}$ is the required rectangle. View full question & answer→Question 163 Marks
Construct a rectangle $\text{ABCD},$ when:One side $= 4 \ cm $ and one diagonal is $5 \ cm.$ Measure the length of the other side.
Answer
Steps:
$1.$ Draw $BC=4 \ cm$.
$2.$ With $C$ as a center and radius $5 \ cm$ draw an arc at $A$.
$3.$ Now join $AB$ and $AC$.
$4.$ With $A$ as a center draw an arc at $D.$
$5.$ Now join $AD$ and $CD.$
$\text{ABCD}$ is the required rectangle. View full question & answer→Question 173 Marks
Construct a parallelogram $\text{ABCD},$ when$:AB = 4.5 \ cm, \angle B = 120^\circ $ and the distance between $AB$ and $DC = 3.0 \ cm.$
Answer
Steps:
$1.$ Draw $A B=4.5 \ cm$.
$2. $At $B$, draw $BP \perp AB$.
$3.$ From $BP$ cut $BE =3 \ cm$.
$4.$ Through $E$ draw a perpendicular to $BP$ to get $QR$ parallel to $AB$.
$5.$ With $B$ as a center draw an arc that cuts $Q R$ at $C$.
$6.$ With $A$ as a center draw an arc that cuts $Q R$ at $D$.
$7.$ Now join $AD$ and $BC$.
$\text{ABCD}$ is the required parallelogram. View full question & answer→Question 183 Marks
Construct a parallelogram $\text{ABCD},$ when$:AB = 6.0 \ cm, AD = 5.0 \ cm$ and $\angle A = 45^\circ .$
Answer
Steps:
$1.$ Draw $AB=6\ cm$.
$2.$ Draw $AD$ with radii $5\ cm$ with an angle of $45^{\circ}$.
$3.$ With $D$ and $B$ as a center and radii $6 \ cm$ and $5\ cm$ draw arcs cutting each other at $C$.
$4.$ Now join $DC$ and $BC$.
$\text{ABCD}$ is the required parallelogram. View full question & answer→