# Practical Geometry

## Exercise 4.3

### Construct the following quadrilaterals

Question 1: Quadrilateral MORE

MO = 6 cm, OR = 4.5 cm, ∠M = 60°, ∠O = 105°, ∠R = 105°

**Answer:** Steps are as follows:

- Draw MO = 6 cm
- Make an angle = 105° at point O.
- Draw OR = 4.5 cm
- Make an angle = 105° at point R
- Make and angle = 60° at point M
- Extend lines from points M and R so that they intersect at point E.
- Quadrilateral MORE is complete.

Here, sum of given three angles of given quadrilateral is = 60 + 105 + 105 = 270

So, fourth angle = 360 – 270 = 90

Question 2: Quadrilateral PLAN

PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°

**Answer:** Steps are as follows:

- Calculate fourth angle, i.e. ∠L = 360 – (90 + 110 + 85)

= 360 – 285 = 75 - Draw PL = 4 cm
- Make an angle of 90° on point P and another angle of 75° on point L.
- Draw LA = 6.5 cm
- Make an angle of 110° on point A
- Extend lines from P and A so that they intersect at point P
- Quadrilateral PLAN is complete.

Question 3: Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = 85°

**Answer:** Steps are as follows:

- Draw HE = 5 cm
- Make an angle of 85° on point E
- Draw EA = 6 cm
- We know that adjacent angles are supplementary in a parallelogram.
- Supplement of 85° = 180° - 85° = 95°
- Make and angle of 95° on point A
- Draw AR = 5 cm so that it is parallel to HE
- Join H to R
- Parallelogram HEAR is complete.

Question 4: Rectangle OKAY

OK = 7 cm, KA = 5 cm

**Answer:** All angles of a rectangle are right angles and opposite sides are equal.

- Draw OK = 7 cm
- Draw KA = 5 cm perpendicular to OK
- Draw AY = 7 cm perpendicular to KA
- Join O to Y
- Rectangle OKAY is complete.

## Exercise 4.4

##### Construct the following quadrilaterals

Question 1: Quadrilateral DEAR

DE = 4 cm, EA = 5 cm, AR = 4.5 cm, ∠E = 60°, ∠A = 90°

**Answer:** Steps are as follows:

- Draw DE = 4 cm
- Make and angle of 60° on point E
- Draw EA = 5 cm
- Make a right angle at point A
- Draw AR = 4.5 cm
- Join D to R
- Quadrilateral DEAR is complete

Question 2: Quadrilateral TRUE

TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠R = 75°, ∠U = 120°

**Answer:** Steps are as follows:

- Draw TR = 3.5 cm
- Make an angle of 75° on point R
- Draw RU = 3 cm
- Make an angle of 120° on point U
- Draw UE = 4 cm
- Join T to E
- Quadrilateral TRUE is complete

## Exercise 4.5

### Draw the following

Question 1: The square READ with RE = 5.1 cm

**Answer:** All sides of a square are equal and all angles are right angle.

- Draw RE = 5.1 cm
- Draw EA = 5.1 cm perpendicular to RE
- Draw DA = 5.1 cm perpendicular to EA
- Join R to D
- Square READ is complete.

Question 2: A rhombus whose diagonals are 5.2 cm and 6.4 cm long

**Answer:** We know that diagonals of a rhombus are perpendicular bisectors of each other

- Draw a vertical line = 6.4 cm
- Draw the perpendicular bisector of this line of length 5.2 cm
- Join four vertices to complete the rhombus

Question 3: A rectangle with adjacent sides of lengths 5 cm and 4 cm

**Answer:** All angles of a rectangle are right angles and opposite sides are equal.

- Draw a horizontal line = 5 cm
- Draw another line which is perpendicular to previous line and its length = 4 cm
- Draw a third line which is perpendicular to second line with length = 5 cm
- Draw a fourth line which is perpendicular to third line.
- Rectangle is complete.

Question 4: A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

**Answer:** Steps are as follows:

- Draw OK = 5.5 cm
- Draw KA = 4.5 cm at any angle
- Draw YA||OK
- Draw OY||KA
- Parallelogram is complete.

This is not a unique parallelogram, because different parallelograms can be made by changing the value of the angle between first two lines.