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:

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:

Question 3: Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = 85°

Quadrilateral

Answer: Steps are as follows:

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.

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:

Question 2: Quadrilateral TRUE

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

Quadrilateral

Answer: Steps are as follows:


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.

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

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.

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

Quadrilateral

Answer: Steps are as follows:

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



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