## Chapter 4 Practical Geometry Exercise 4.5

Draw the following.

Question 1: The square READ with RE = 5.1 cm.

Answer:

Given

Square READ

RE = 5.1 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment DA = 5.1 cm.

2. Make ∠XDA = 90°.

3. Make ∠YAD = 90°.

4. With D as centre, radius 5.1 cm draw an arc to cut ray XD at R.

5. With A as centre, radius 5.1 cm draw an arc to cut ray YA at E.

6. Join R and E.

7. READ is the required quadrilateral.

Question 2: A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Answer:

Given

Rhombus

Diagonals = 5.2 cm, 6.4 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment UA = 6.4 cm.

2. Draw the perpendicular bisector of UA at O. (O is the midpoint of UA).

3. With O as centre, radius 2.6 cm draw arcs on either sides to intersect the perpendicular bisector at R and M.

4. Join RU, RA, UM, AM.

5. RAMU is the required rhombus.

Question 3: A rectangle with adjacent sides of lengths 5 cm and 4 cm.

Answer:

Given

Rectangle

Length = 5 cm

Breadth = 4 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment DA = 5 cm.

2. Make ∠XDA = 90°.

3. Make ∠YAD = 90°.

4. With D as centre, radius 4 cm draw an arc to cut ray XD at R.

5. With A as centre, radius 4 cm draw an arc to cut ray YA at E.

6. Join R and E.

7. READ is the required rectangle.

Question 4: A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm.

Answer:

To draw any quadrilateral, five measurements would be required. This would be possible when

• When four sides and one diagonal are given.

• When two diagonals and three sides are given.

• When two adjacent sides and three angles are given.

• When three sides and two included angles are given.

• When other special properties are known.

But in parallelogram OKAY only 4 measures are given (opposite sides are equal). So any 1 measurement can be useful for making this parallelogram. It may include angle between the sides or one diagonal. Therefore, this parallelogram can’t be drawn.

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