# Practical Geometry

## Exercise 4.1

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

• 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

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

• 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

Question 3: Parallelogram MORE

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

• 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

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

• 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.

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

• 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