Geometrical Constructions Maths - Geometrical Constructions

Take some round bowls and plates. Place their edges one upon the other to find pairs of congruent edges.

Find congruent circles in your surroundings.

Get bangles of different sizes but equal thickness and find the congruent ones among them.

Take a rectangular paper. Place two opposite sides upon each Other. What do you observe?

From the shape shown below, write the names of the pairs of congruent line segments.
i. seg AB ≅ seg DC
ii. seg AE ≅ seg BH
iii. seg EF ≅ seg ___
iv. seg DF ≅ seg ___

Observe the image shown in the adjacent figure and answer the following questions.

1. What time does this clock show ?
2. What is the measure of the angle between its two hands ?
3. At which other times is the angle between the hands congruent with this angle ?
   

Observe the given angles and write the names of those having equal measures.

Some angles are given below. Using the symbol of congruence write the names of the pairs of congruent angles in these figures.

Draw ∆ABC such that l(BC) = 8 cm, l(CA) = 6 cm, m∠ABC = 40°.
Draw a ray to make an angle of 40° with the base BC, l(BC) = 8 cm. We have to obtain point ‘A’ on the ray. With ‘C’ as the centre, draw an arc of radius 6 cm to do so. What do we observe? The arc intersects the ray in two different points. Thus, we get two triangles of two different shapes having the given measures

Draw triangles with the measures given below:
In ∆PQR, l(PQ) = 6 cm, l(QR) = 3.8 cm, l(PR) = 4.5 cm.

Draw triangles with the measures given below:
In ∆STU, l(ST) = 7 cm, l(TU) = 4 cm, l(SU) = 5 cm.

Draw triangles with the measures given below:
In ∆ABC, l(AB) = 5.5 cm, l(BC) = 4.2 cm, l(AC) = 3.5 cm.

Students should take examples of their own and practice construction of triangles.
i. In ∆PQR, l(PQ) = 5 cm, l(QR) = 6.8 cm, l(PR) = 5.5 cm.
ii. In ∆XYZ, l(XY) = 5.7 cm, m∠Y = 120°, l(YZ) = 7 cm.
iii. In ∆RST, l(ST) = 6.7 cm, m∠S = 60°, m∠T = 40°.
iv. In ∆UVW, m∠U = 90°, l(UV) = 5 cm, l(VW) = 6 cm.

Draw triangle with the measures given. In ∆PQR, l(PQ) = 4.5 cm, l(PR) = 11.7cm, m∠PQR = 90°.

Draw triangle with the measures given. In ∆ABC, l(AC) = 7.5 cm, m∠ABC = 90°, l(BC) = 5.5cm.

Draw triangle with the measures given. In the right-angled ∆STU, hypotenuse SU = 5cm and l(ST) = 4cm.

Draw triangle with the measures given. In ∆MAN, m∠MAN = 90°, l(AN) = 8 cm, l(MN) = 10 cm.

Draw triangle with the measures given. In ∆XYZ, l(XY) = 7.3 cm, m∠X = 34°, m∠Y = 95°.

Draw triangle with the measures given. In ∆EFG, l(EG) = 6 cm, m∠F = 65°, m∠G = 45°.

Draw triangle with the measures given. In ∆MNP, l(NP) = 5.2 cm, m∠N = 70°, m∠P = 40°

Draw triangle with the measures given. In ∆SAT, l(AT) = 6.4 cm, m∠A = 45°, m∠T = 105°.

Draw an equilateral triangle with side 6.5 cm.