Construct a $\triangle$ABC in which BC = 6 cm AC = 5.6 cm and AB=7.6 cm. Construct a parallelogram equal in area to $\triangle$ABC and having an angle 75$^o$.

Construct a triangle ABC in which AB = 6 cm, BC = 7.2 cm, and $\angle$B = 60$^{o}$. Construct a parallelogram equal in area to the triangle ABC with an angle 60$^o$.

Construct a $\triangle$ABC in which a = 7.8 cm b = 7.2 cm and c = 6.3 cm. Construct a parallelogram equal in area to $\triangle$ABC and having a side 8 cm. 

Construct a $\triangle$ABC in which b = 5 cm, c = 4.8 cm and $\angle$ABC=45$^{o}$. Construct a parallelogram CDEF equal in area to $\triangle$ABC and having a side (CD) = 7.5 cm.

Construct a triangle having one angle equal to 45$^{\circ}$ and equal in area to the parallelogram ABCD having BC = 5 cm and AB = 4 cm and $\angle$B=60$^{\circ}$.

Construct a triangle having an equal area to the parallelogram ABCD with AB = 6 cm, BC = 7.5 cm, and $\triangle$ABC=60$^{\circ}$.

Construct a triangle equal in area to the parallelogram ABCD having sides AB = 5 cm, AD = 6 cm and the diagonal BD =6 cm.

Construct a triangle equal in area to the parallelogram ABCD having two diagonals 6 cm and 4.8 cm respectively and the angle between them is 30$^{\circ}$.

Construct a triangle equal in area to the parallelogram ABCD having two diagonals 4 cm and 5 cm respectively and the angle between them is 45°.

Construct a quadrilateral ABCD in which AB = BC = 5.6 cm, CD = AD = 4.9 cm, and $\angle$BAD = 60°. Construct a triangle equal in area to the quadrilateral ABCD.

Construct a quadrilateral ABCD having an AB = 5.1 cm, BC = 4.9 cm, CD = 5.5 cm, AD = 6.1 cm, and BD = 5.3 cm then construct a triangle equal in area to the quadrilateral.

Construct a quadrilateral ABCD in which AB = 8 cm, BC = 3.5 cm, CD =7 cm, DA = 6  cm, and $\angle$BAD = 60$^{\circ}$. Also, construct a triangle equal in area to the quadrilateral.

Construct a quadrilateral PQRS in which PQ = 6.5 cm, QR = 5.8 cm, SR =7 cm, PS=4.5 cm, and $\angle$QPS=60$^{\circ}$. Also, construct a triangle equal in area to the quadrilateral.

Construct a quadrilateral ABCD having given data, AB = BC= 5.5cm, CD = DA = 4.5 cm and $\angle$A=75$^{\circ}$. Construct a triangle equal in area of this quadrilateral.

Construct a rectangle equal in area to a triangle ABC in which AB = 6.5 cm, BC =7.6 cm, and CA = 6.9 cm.

Construct a triangle ABC in which AB = 6 cm, BC = 7 cm, and CA = 4 cm. Also construct a rectangle equal in area to the triangle ABC.

Construct a triangle ABC in which a = 4 cm, b = 5.2 cm, and c = 3.5 cm. Also, construct a rectangle equal in area to the triangle ABC.

Construct a triangle having an angle 60$^{\circ}$ and whose area equals to the rectangle having a length of 6 cm and breadth 4.5 cm.

Construct a parallelogram having one angle equal to 45$^{\circ}$ and equal in area to the parallelogram ABCD having BC = 5 cm and AB = 4 cm and $\angle$B=60$^{\circ}$.

Construct a parallelogram having one angle 45$^{\circ}$ and in equal area to the parallelogram ABCD with AB = 6 cm, BC =7.5 cm and $\angle $ABC=60$^{\circ}$.

Construct a parallelogram having an angle of 75$^{\circ}$ and equal area to the parallelogram ABCD having sides AB = 5 cm, AD = 6 cm, and the diagonal BD = 6 cm.

Construct a parallelogram having a side 7.2 cm and equal area to the parallelogram ABCD having two diagonals 6 cm and 4.8 cm respectively and angle between them 30$^{\circ}$.

Construct a $\triangle$ABC in which AB = 5 cm, BC = 6 cm, and $\angle$ABC = 60$^{\circ}$. Also, construct another $\triangle$DBC which is equal in area to the $\triangle$ABC such that DB = 8.4 cm.

Construct a $\triangle$ABC in which AB = 4.5 cm, BC = 5.6 cm and $\angle$ABC = 60$^{\circ}$. Also, construct another $\triangle$DBC which is equal in area to the $\triangle$ABC such that DB = 7.5 cm.

Construct a $\triangle$ABC in which BC = 6.4 cm, AB = 5.6 cm, and AC = 6 cm. Also, construct another $\triangle$DBC having an angle 60$^{\circ}$ and is equal in area to the $\triangle$ABC. 

Construct a $\triangle$LMN in which LM = 6.3 cm, $\angle$LNM=30$^{\circ}$ and $\angle$LMN=45$^{\circ}$. Also, construct another $\triangle$OLM having OL = 7.5 cm.

Construct a parallelogram having a side 5.5 cm and whose area is equal to a rectangle of length 6.5 cm and breadth 5 cm.

Construct a parallelogram in which one side AB = 5.5 cm. , diagonal AC = 8 cm, and diagonal BD = 6 cm. Construct a rectangle having equal area to this parallelogram.

Construct a quadrilateral ABCD in which AB=4.5cm, AC=CD=5cm, AD=6cm, and $\angle$BAC=60$^{\circ}$. Also, construct a triangle PBC whose area is equal to the area of the quadrilateral. Give the reason for being the area of the quadrilateral ABCD and the triangle PBC equal.

In the adjoining figure, NS//AM and NA//KM. NK is extended to the point S.

1. Write the name of two triangles having equal area.
2. Prove that: $\rm \triangle PAM = \frac {1}{2}$parallelogram $\rm AMKN$

In the given figure, PQRS is a square in which PR=10cm. PS is produced to T. What is the area of $\triangle$QRT so formed? Find it.

In a circle with centre O, circumference angles RMP and RNP are drawn on the same arc RP. $\angle$ROP is the central angle.

1. Write the relation between $\angle$RMP and $\angle$RNP.
2. If $\angle$MRN=(7x-2)$^{\circ}$ and $\angle$MPN=(3x+10)$^{\circ}$, find the value of $\angle$MRN.
3. Verify experimentally that the relation between $\angle$RMP and $\angle$ROP after drawing two circles having radii at least 3 cm.

In the given figure, AB is the height of a boy, and a point C is the position of a flying kite in
the sky. AC is the length of the string of the kite.

1. Define angle of elevation
2. If $\angle$CAH =30$^{\circ}$, what is the value of CH? Find it.
3. Find the height of the kite flying in the sky.
4. If the measure of $\angle$CAH be changed from 30$^{\circ}$ to 45$^{\circ}$, at what height the kite fly than the previous height ? Find it.

Triangle PQT and parallelogram PQRS are standing on the same base PQ and between the same parallel lines PQ and ST.

1. Write the relationship between the area of parallelogram and area of triangle standing on the same base and between the same parallel lines.
2. If the length of base of parallelogram PQRS is 12 cm with height 8 cm, find the area of $\triangle$PQT.

In a $\rm \triangle $ABC, $\rm \angle $ABC=60°, BC=4.4 cm and AB = 5.2 cm are given.

1. Construct a $\rm \triangle$ABC according to above measurements, then construct a rectangle MNOC equal in area to the triangle.
2. Why the areas of triangle and rectangle so formed are equal? Write reason. 

In the figure, two circles are intersected at the points P and Q. Two lines AB and CD pass through the point Q.

1. What is the relation between the inscribed angles made by the same arc? Write it. 
2. If $\rm \angle$ QAP =  25$^{\circ}$ and $\rm \angle$ QCP =  (2x - 15)$^{\circ}$, find the value of x.
3. Prove that: $\rm \angle $CPA = $\rm \angle $BPD.
4. Verify experimentally that the central angle is double of the inscribed angle standing on the same arc by making two circles having at least 3 cm radii. 

A tree is broken by wind. The top of the broken part without detaching makes an angle of 30$\circ$ with the ground. The distance from the foot of the tree to the point on the ground where the top of the tree touches the ground is $\rm 9\sqrt 3$ m.

1. Define angle of elevation.
2. Sketch the figure from the above context.
3. Find the length of the broken part of the tree.
4. If the length of the remaining part of the tree after broken is also $9\sqrt 3$ meter, what angle will the top of the tree make with the ground? Write reason.

Construct a $\triangle$ABC in which BC = 6 cm AC = 5.6 cm and AB=7.6 cm. Construct a parallelogram equal in area to $\triangle$ABC and having an angle 75$^o$.

Construct a triangle ABC in which AB = 6 cm, BC = 7.2 cm, and $\angle$B = 60$^{o}$. Construct a parallelogram equal in area to the triangle ABC with an angle 60$^o$.

Construct a $\triangle$ABC in which a = 7.8 cm b = 7.2 cm and c = 6.3 cm. Construct a parallelogram equal in area to $\triangle$ABC and having a side 8 cm. 

Construct a $\triangle$ABC in which b = 5 cm, c = 4.8 cm and $\angle$ABC=45$^{o}$. Construct a parallelogram CDEF equal in area to $\triangle$ABC and having a side (CD) = 7.5 cm.

Construct a triangle having one angle equal to 45$^{\circ}$ and equal in area to the parallelogram ABCD having BC = 5 cm and AB = 4 cm and $\angle$B=60$^{\circ}$.

Construct a triangle having an equal area to the parallelogram ABCD with AB = 6 cm, BC = 7.5 cm, and $\triangle$ABC=60$^{\circ}$.

Construct a triangle equal in area to the parallelogram ABCD having sides AB = 5 cm, AD = 6 cm and the diagonal BD =6 cm.

Construct a triangle equal in area to the parallelogram ABCD having two diagonals 6 cm and 4.8 cm respectively and the angle between them is 30$^{\circ}$.

Construct a triangle equal in area to the parallelogram ABCD having two diagonals 4 cm and 5 cm respectively and the angle between them is 45°.

Construct a quadrilateral ABCD in which AB = BC = 5.6 cm, CD = AD = 4.9 cm, and $\angle$BAD = 60°. Construct a triangle equal in area to the quadrilateral ABCD.

Construct a quadrilateral ABCD having an AB = 5.1 cm, BC = 4.9 cm, CD = 5.5 cm, AD = 6.1 cm, and BD = 5.3 cm then construct a triangle equal in area to the quadrilateral.

Construct a quadrilateral ABCD in which AB = 8 cm, BC = 3.5 cm, CD =7 cm, DA = 6  cm, and $\angle$BAD = 60$^{\circ}$. Also, construct a triangle equal in area to the quadrilateral.

Construct a quadrilateral PQRS in which PQ = 6.5 cm, QR = 5.8 cm, SR =7 cm, PS=4.5 cm, and $\angle$QPS=60$^{\circ}$. Also, construct a triangle equal in area to the quadrilateral.

Construct a quadrilateral ABCD having given data, AB = BC= 5.5cm, CD = DA = 4.5 cm and $\angle$A=75$^{\circ}$. Construct a triangle equal in area of this quadrilateral.

Construct a rectangle equal in area to a triangle ABC in which AB = 6.5 cm, BC =7.6 cm, and CA = 6.9 cm.

Construct a triangle ABC in which AB = 6 cm, BC = 7 cm, and CA = 4 cm. Also construct a rectangle equal in area to the triangle ABC.

Construct a triangle ABC in which a = 4 cm, b = 5.2 cm, and c = 3.5 cm. Also, construct a rectangle equal in area to the triangle ABC.

Construct a triangle having an angle 60$^{\circ}$ and whose area equals to the rectangle having a length of 6 cm and breadth 4.5 cm.

Construct a parallelogram having one angle equal to 45$^{\circ}$ and equal in area to the parallelogram ABCD having BC = 5 cm and AB = 4 cm and $\angle$B=60$^{\circ}$.

Construct a parallelogram having one angle 45$^{\circ}$ and in equal area to the parallelogram ABCD with AB = 6 cm, BC =7.5 cm and $\angle $ABC=60$^{\circ}$.

Construct a parallelogram having an angle of 75$^{\circ}$ and equal area to the parallelogram ABCD having sides AB = 5 cm, AD = 6 cm, and the diagonal BD = 6 cm.

Construct a parallelogram having a side 7.2 cm and equal area to the parallelogram ABCD having two diagonals 6 cm and 4.8 cm respectively and angle between them 30$^{\circ}$.

Construct a $\triangle$ABC in which AB = 5 cm, BC = 6 cm, and $\angle$ABC = 60$^{\circ}$. Also, construct another $\triangle$DBC which is equal in area to the $\triangle$ABC such that DB = 8.4 cm.

Construct a $\triangle$ABC in which AB = 4.5 cm, BC = 5.6 cm and $\angle$ABC = 60$^{\circ}$. Also, construct another $\triangle$DBC which is equal in area to the $\triangle$ABC such that DB = 7.5 cm.

Construct a $\triangle$ABC in which BC = 6.4 cm, AB = 5.6 cm, and AC = 6 cm. Also, construct another $\triangle$DBC having an angle 60$^{\circ}$ and is equal in area to the $\triangle$ABC. 

Construct a $\triangle$LMN in which LM = 6.3 cm, $\angle$LNM=30$^{\circ}$ and $\angle$LMN=45$^{\circ}$. Also, construct another $\triangle$OLM having OL = 7.5 cm.

Construct a parallelogram having a side 5.5 cm and whose area is equal to a rectangle of length 6.5 cm and breadth 5 cm.

Construct a parallelogram in which one side AB = 5.5 cm. , diagonal AC = 8 cm, and diagonal BD = 6 cm. Construct a rectangle having equal area to this parallelogram.

Construct a quadrilateral ABCD in which AB=4.5cm, AC=CD=5cm, AD=6cm, and $\angle$BAC=60$^{\circ}$. Also, construct a triangle PBC whose area is equal to the area of the quadrilateral. Give the reason for being the area of the quadrilateral ABCD and the triangle PBC equal.

In the adjoining figure, NS//AM and NA//KM. NK is extended to the point S.

1. Write the name of two triangles having equal area.
2. Prove that: $\rm \triangle PAM = \frac {1}{2}$parallelogram $\rm AMKN$

In the given figure, PQRS is a square in which PR=10cm. PS is produced to T. What is the area of $\triangle$QRT so formed? Find it.

In a circle with centre O, circumference angles RMP and RNP are drawn on the same arc RP. $\angle$ROP is the central angle.

1. Write the relation between $\angle$RMP and $\angle$RNP.
2. If $\angle$MRN=(7x-2)$^{\circ}$ and $\angle$MPN=(3x+10)$^{\circ}$, find the value of $\angle$MRN.
3. Verify experimentally that the relation between $\angle$RMP and $\angle$ROP after drawing two circles having radii at least 3 cm.

In the given figure, AB is the height of a boy, and a point C is the position of a flying kite in
the sky. AC is the length of the string of the kite.

1. Define angle of elevation
2. If $\angle$CAH =30$^{\circ}$, what is the value of CH? Find it.
3. Find the height of the kite flying in the sky.
4. If the measure of $\angle$CAH be changed from 30$^{\circ}$ to 45$^{\circ}$, at what height the kite fly than the previous height ? Find it.

Triangle PQT and parallelogram PQRS are standing on the same base PQ and between the same parallel lines PQ and ST.

1. Write the relationship between the area of parallelogram and area of triangle standing on the same base and between the same parallel lines.
2. If the length of base of parallelogram PQRS is 12 cm with height 8 cm, find the area of $\triangle$PQT.

In a $\rm \triangle $ABC, $\rm \angle $ABC=60°, BC=4.4 cm and AB = 5.2 cm are given.

1. Construct a $\rm \triangle$ABC according to above measurements, then construct a rectangle MNOC equal in area to the triangle.
2. Why the areas of triangle and rectangle so formed are equal? Write reason. 

In the figure, two circles are intersected at the points P and Q. Two lines AB and CD pass through the point Q.

1. What is the relation between the inscribed angles made by the same arc? Write it. 
2. If $\rm \angle$ QAP =  25$^{\circ}$ and $\rm \angle$ QCP =  (2x - 15)$^{\circ}$, find the value of x.
3. Prove that: $\rm \angle $CPA = $\rm \angle $BPD.
4. Verify experimentally that the central angle is double of the inscribed angle standing on the same arc by making two circles having at least 3 cm radii. 

A tree is broken by wind. The top of the broken part without detaching makes an angle of 30$\circ$ with the ground. The distance from the foot of the tree to the point on the ground where the top of the tree touches the ground is $\rm 9\sqrt 3$ m.

1. Define angle of elevation.
2. Sketch the figure from the above context.
3. Find the length of the broken part of the tree.
4. If the length of the remaining part of the tree after broken is also $9\sqrt 3$ meter, what angle will the top of the tree make with the ground? Write reason.