Practical Geometry

Exercise 4.1

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.

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.