Question

Complete the activity according to the given steps.

1. Draw rhombus ABCD. Draw diagonal AC.
2. Show the congruent parts in the figure by identical marks.
3. State by which test and in which correspondence ΔADC and ΔABC are congruent.
4. Give reason to show ∠DCA ≅ ∠BCA and ∠DAC ≅ ∠BAC
5. 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]

The attribute of a rhombus revealed by the preceding phases is 'diagonal of a rhombus bisect the opposite angles'.