# Practical Geometry

## Exercise 4.1

### Construct the following quadrilaterals

Question 1: Quadrilateral ABCD

AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm, AC = 7 cm

**Answer:** Steps are as follows:

- Draw diagonal AC = 7 cm
- From point A, make an arc at 4.5 cm
- From point C, make an arc at 5.5 cm so that it intersects the previous arc. This is point B
- Join B to A and C to get AB and BC
- From point A, make an arc at 6 cm on another side of diagonal.
- From point C, make an arc at 4 cm so that it intersects the previous arc. This is point D.
- Join D to A and C to get AD and CD
- Quadrilateral ABCD is complete.

Question 2: Quadrilateral JUMP

JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm

**Answer:** Steps are as follows:

- Draw the diagonal PU = 6.5 cm
- From point P, make an arc at 4.5 cm
- From point U, make an arc at 3.4 cm so that it intersects the previous arc. This is point J
- Join J to P and U to get PJ and JU
- From point P, make an arc at 5 cm on another side of diagonal.
- Form point U, make an arc at 4 cm to intersect previous arc. This is point M
- Join M to P and U, to get PM and UM
- Quadrilateral JUMP is complete.

Question 3: Parallelogram MORE

OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm

**Answer:** Steps are as follows:

- Draw diagonal EO = 7.5 cm
- From point O, make and arc at 6 cm.
- From point E, make an arc at 4.5 so that it intersects previous arc. This is point R.
- Join R to O and E to get OR and OE, and to get ΔROE
- From point E, make an arc at 6 cm on another side of diagonal.
- From point O, make an arc at 4.5 cm so that it intersects previous arc. This is point M.
- Join M to O and E to get OM and EM.
- Parallelogram MORE is complete.

Question 4: Rhombus BEST

BE = 4.5 cm, ET = 6 cm

**Answer:** We know that all sides of rhombus are equal.

- Draw ET = 6 cm
- From point E, make an arc at 4.5 cm
- From point T, make an arc at 4.5 cm so that it intersects previous arc. This is point B.
- Join B to E and T, to get BE and BT.
- From point E, make an arc at 4.5 cm on another side of diagonal
- From point T, make an arc at 4.5 cm so that it intersects previous arc. This is point S.
- Join S to E and T, to get SE and ST
- Rhombus BEST is complete.

## Exercise 4.2

### Construct the following quadrilaterals

Question 1: Quadrilateral LIFT

LI = 4 cm, IF = 3cm, TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm

**Answer:** Steps are as follows:

- Draw diagonal LF = 4.5 cm
- From point L, make and arc at 4 cm
- From point F, make an arc at 3 cm so that it intersects previous arc. This is point I
- Join I to L and F to get LI and IF
- From point L, make an arc at 2.5 cm on another side of diagonal.
- From point F, make an arc at 4 cm so that it intersects previous arc. This is point T.
- Join T to L and F to get TL and FT.
- Quadrilateral LIFT is complete.

Question 2: Quadrilateral GOLD

OL = 7.5 cm, GL = 4 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm

**Answer:** Steps are as follows:

- Draw diagonal GL = 4 cm
- From point G, make an arc at 10 cm.
- From point L, make an arc at 7.5 cm so that it intersects previous arc. This is point O.
- Join O to G and L to get GO and OL
- From point G, make an arc at 6 cm, on another side of diagonal.
- Form point L, make an arc at 5 cm so that it intersects previous arc. This is point D.
- Join D to G and L to get DG and LD
- Quadrilateral GOLD is complete.

Question 3: Rhombus BEND

BN = 5.6 cm, DE = 6.5 cm

**Answer:** Diagonals of a rhombus are perpendicular bisectors of each other.

- Draw DE = 6.5 cm
- Draw the perpendicular bisector of DE, so that the bisector = BN = 5.6 cm
- Join four vertices to complete the rhombus BEND.