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 ∆ ADC and ∆ ABC 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.

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Solution

(1)

(2)

(3) In ∆ ADC and ∆ ABC
AC = AC (Common)
AD = AB (ABCD is a rhombus so all sides are equal)
DC = BC (ABCD is a rhombus so all sides are equal)
So, by SSS congruency ∆ ADC is congruent to ∆ ABC
(4) Since ∆ ADC is congruent to ∆ ABC so,
∠DCA ≌ ∠BCA and ∠DAC ≌ ∠BAC by CPCT (corresponding parts of congruent triangles)
(5) Since ∠DCA ≌ ∠BCA and ∠DAC ≌ ∠BAC so, AC acts as the angle bisector.
Thus, we can say that diagonals of a rhombus act as angle bisectors.

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