Construction of Parallelogram When Two Adjacent Sides and One Diagonal Are Given.

Q.

Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.

Q.

Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm. Measure the other side.

Q.

Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.

Q.

By following these steps of construction,

(i) Draw a line segment PQ = 11 cm

(ii) At P construct an angle of 60^o and at Q, an angle of 45^o.

(iii) Bisect these angles. Let the bisectors of these angles intersect at a point A.

(iv) Draw perpendicular bisectors DE of AP to intersect PQ at B and FG of AQ to intersect PQ at C.

(v). Join AB and AC. Triangle ABC has been obtained. In this ∆ABC,

1. AB + BC + CA > 11cm

2. AB + BC = 11cm

3. BC + CA = 11cm

4. AB + BC + CA = 11cm

Q. Construct a parallelogram $ABCD$ with $AB=6cm,CD=4.5cm$ and $BD=7.5cm$

Q. Construct parallelogram $ABCD$ with the following measurements:
$AD=4.3cm$, $DC=5.7cm$, $DB=7cm$

Q. Construct a cyclic quadrilateral EFGH with EF$=5.2$cm, $\angle$GEF$={50}^o$, FG$=6$cm and $\angle$EGH$={40}^o$.

Q.

Parallelogram with adjacent sides 7 centimetres and 4 centimetres; one diagonal 8 centimetres.

Q. Construct a parallelogram ABCD, in which AB = 6 cm , BC = 4.2 cm and the height from AB = 3.5 cm.

Q.

Constructing 2 rays, divide a line segment AB of any legth in the ratio 6:2.

Q. Construct the parallelograms with the given measurements and find their area.
CAMP, CA = 6 cm, AP = 8 cm and CP = 5.5 cm.
$\left[5\right]$

Q. Construct a parallelogram MARK in which $MA=5cm,\angle A={110}^o,\angle RMA={35}^o$.

Q. Construct parallelogram $ABCD$ with the following measurements:
$AC=6.8cm$, $DB=7.6cm$, $AD=6.4cm$

Q. $A(2,1),B(-1,2)$ and $C(1,0)$ are three of the four vertices of parallelogram $ABCD$ Find the coordinates of the fourth vertex $D$.

Q. Construct a quadrilateral $ABCD$, when :

Q. Construct a parallelogram $ABCD$ in which $AB=5.2cm,BC=4.7cm$ and $AC=7.6cm$.

Q. In parallelogram $ABCD$, $E$ and $F$ are midpoints of the sides $AB$ and $CD$ respectively. The line segments $AF$ and $BF$ meet the line segments $ED$ and $EC$ at points $G$ and $H$ respectively.
Prove that:
(i) triangles $HEB$ and $FHC$ are congruent
(ii) $GEHF$ is a parallelogram

Q. The $1^{st}$ step will be:

1. $\left(i\right)$
2. $\left(iii\right)$
3. $\left(ii\right)$
4. $\left(iv\right)$

Q. Question 195
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

Q.

Which property of a parallelogram do we use to construct a parallelogram given its sides and one diagonal?

1. Diagonals are not equal
   

2. Opposite sides are equal
   

3. Diagonals bisect each other
   

4. Opposite sides are parallel

Q. Can you draw the following? Give reasons.
A parallelogram $HOTS$ where $HO=5cm,OT=6cm$ and $OS=5.5cm$

Q.

Construct a parallelogram ABCD such that AB = 4.8 cm, BC = 4 cm and diagonal BD = 5.4 cm.

Q. Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.

Q. Construct a parallelogram ABCD with AB = 8 cm, AD = 7 cm and BD = 9 cmand find its area.

Q. Diagonal AC$=$6.4 cm, AB $=$ 5 cm and side BC$=$ 6 cm construct a parallelogram

Q. Construct $\square LMNO$ such that l(LM) = l(LO) = 6 cm, l(ON) = l(NM) = 4.5cm, l(OM) = 7.5 cm.

Q. Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.