Measure the opposite angles of the quadrilateral and angles at the point M.

Question

Draw a rhombus EFGH by taking convenient length of side and convenient measure of an angle. 

Draw its diagonals and name their point of Intersection as M.

i. Measure the opposite angles of the quadrilateral and angles at the point M. 

ii. Measure the two parts of every angle made by the diagonal.

iii. Measure the lengths of both diagonals. Measure the two parts of diagonals made by point M.

Observe the measures. Also observe the measures obtained by your classmates and discuss about them.

Answer 1

Draw a rhombus EFGH such that its side is 5 cm and m∠F = 60°.

Steps of construction:

i. As shown in the rough figure, draw seg FG of length 5 cm. 

ii. Placing the centre of the protractor at point F, draw ray FX making an angle 60° with seg FG. 

iii. By taking a distance of 5 cm on the compass and placing it at point F, draw an arc on ray FX. Name the point as E.

iv. By taking a distance of 5 cm on the compass and placing it at point E and point G, draw arcs. Name the point of intersection of arcs as H. EFGH is the required rhombus.

From the figure, 

i. Opposite angles: 

m∠EFG = m∠GHE = 60°, 

m∠FEH = m∠HGF = 120° 

Angles at the point M: 

m∠EMF = m∠FMG = m∠GMH = m∠HME = 90°

ii. Angles made by diagonal FH: 

m∠EFH = m∠GFH = 30° m∠EHF = m∠GHF = 30° 

Angles made by diagonal EG: 

m∠FEG = m∠HEG = 60° m∠FGE = m∠HGE = 60°

iii. l(FH) ≈ 8.6 cm 

l(EG) = 5 cm 

l(FM) = l(HM) ≈ 4.3 cm 

l(EM) = l(GM) ≈ 2.5 cm

From the above measures, we can say that for any rhombus,

i. Opposite angles are congruent. 

ii. Diagonals bisect the opposite angles. 

iii. Diagonals bisect each other and they are perpendicular to each other.