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 Δ ADC and Δ 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.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The answer of above questions are:--

(1) The rhombus figure is attached below

(2) The congruent parts are shown with || line in the figure

(3) In Δ ADC and Δ ABC we have

AD = AB (all sides equal in rhombus)

AC = AC (common or overlapping side in both triangles)

DC = BC (all sides equal in rhombus)

Hence Δ ADC ≅ Δ ABC (using SSS congruency rule)

(4) Since Δs Δ ADC and Δ ABC are congruent, hence their corresponding angles ∠DCA will be equal to ∠BCA and ∠DAC will be equal to ∠BAC.

(5) It highlights that opposite angles of the rhombus are congruent.