AP State Syllabus AP Board 6th Class Maths Solutions Chapter 10 Practical Geometry Unit Exercise Textbook Questions and Answers.

## AP State Syllabus 6th Class Maths Solutions 10th Lesson Practical Geometry Unit Exercise

Question 1.

Construct a circle with centre X and diameter 10 cm. Sol. Given diameter of circle d = 10 cm

Solution:

We know that radius of circle r = \(\frac{d}{2}=\frac{10}{2}\) = 5

So, radius of the circle is 5 cm.

Now, draw a circle with radius 5 cm.

Question 2.

Draw four circles of radius 2 cm, 3 cm, 4 cm and 5 cm with the same centre P.

Solution:

Radii of four circles are PA = 2cm, PB = 3cm, PC = 4cm and PD = 5cm with the same centre P was constructed.

Question 3.

Draw the angles given below using a protractor.

(i) 75°

(ii) 15°

(iii) 105°

Solution:

(i) 75°

∠ADI = 75°

Steps of construction :

- Draw a ray \(\overrightarrow{\mathrm{DI}}\) with vertex D.
- Place the centre point of the protractor at D and the line be aligned with DI.
- Mark a point A at 75°.
- Join DA. ∠ADI = 75° is formed.

Hence the required angle ∠ADI = 75° is constructed.

ii) 15°

∠KIS = 15°

Steps of construction:

- Draw a ray \(\overrightarrow{\mathrm{IS}}\) with vertex I.
- Place the centre point of the protractor at I and the line be aligned with \(\overrightarrow{\mathrm{IS}}\).
- Mark a point K at 15°.
- Join IK.∠KIS = 15° is formed.

Hence the required angle ∠KIS = 15° is constructed.

(iii) 105°

∠MAD = 105°

Steps of construction:

- Draw a ray \(\overrightarrow{\mathrm{AD}}\) with initial point A.
- Place the centre point of the protractor

at A and the line be aligned with \(\overrightarrow{\mathrm{AD}}\). - Mark a point M at 105°.
- Join AM.∠MAD = 105° is formed.

Hence the required angle∠MAD = 105° ¡s constructed.

Question 4.

Construct ∠ABC = 50° and then draw another angle ∠XYZ equal to ∠ABC without using a protractor.

Solution:

Given ∠ABC = 50° and ∠XYZ = 50°.

Steps of construction:

- Construct ∠ABC = 50°by using protractor.
- By taking any radius draw arcs from B on AB and BC at P and Q respectively.
- Draw a ray \(\overrightarrow{\mathrm{YX}}\) with initial point Y.
- By taking BP as radius draw an arc on \(\overrightarrow{\mathrm{YX}}\) from Y which meets at K.
- Draw arc from Y by taking PQ as radius in the ∠BAC which cuts the previous arc and mark it as L. Now draw \(\overrightarrow{\mathrm{YZ}}\). So, ∠XYZ = 50° is formed.

Hence ∠XYZ = 50° is constructed which is equal to ∠ABC = 50°.

Question 5.

Construct ∠DEF = 60°. Bisect it, measure each half by using a protractor.

Solution:

Given ∠DEF = 60°

Draw EX as the bisector of ∠DEF.

So, ∠DEX = ∠XEF = \(\frac{\angle \mathrm{DEF}}{2}=\frac{60^{\circ}}{2}\) = 30°

∴ ∠DEX = ∠XEF = 30°