Class 8 Maths

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°

Quadrilateral

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°

Quadrilateral

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°

Quadrilateral

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

Quadrilateral

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°

Quadrilateral

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°

Quadrilateral

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

Quadrilateral

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

Quadrilateral

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

Quadrilateral

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?

Quadrilateral

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.