Question

Complete the activity according to the given steps.

i. Draw rhombus ABCD. Draw diagonal AC. 

ii. Show the congruent parts in the figure by identical marks. 

iii. State by which, test and in which correspondence ∆ADC and ∆ABC are congruent. 

iv. Give reason to show ∠DCA ≅ ∠BCA, and ∠DAC ≅ ∠BAC 

v. State which property of a rhombus is revealed from the above steps.

Answer 1

In ∆ADC and ∆ABC,

side AD ≅ side AB …..[Sides of a rhombus] 

side DC ≅ side BC …..[Sides of a rhombus] 

side AC ≅ side AC … [Common side] 

∆ADC ≅ ∆ABC … [By SSS test] 

∠DCA ≅ ∠BCA …[Corresponding angles of congruent triangles] 

∠DAC ≅ ∠BAC …[Corresponding angles of congruent triangles] 

From the above steps, property of rhombus revealed is ‘diagonal of a rhombus bisect the opposite angles’.