Notifications
Clear all
Quadrilaterals
1
Posts
2
Users
0
Likes
345
Views
0
13/07/2021 11:45 am
Topic starter
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
1 Answer
0
13/07/2021 11:46 am
Given that,
ABCD is a rhombus.
AC and BD are its diagonals.
Proof:
AD = CD (Sides of a rhombus)
∠DAC = ∠DCA (Angles opposite of equal sides of a triangle are equal.)
AB || CD
⇒∠DAC = ∠BCA (Alternate interior angles)
⇒∠DCA = ∠BCA
AC bisects ∠C.
Similarly,
We can prove that diagonal AC bisects ∠A.
Following the same method,
We can prove that the diagonal BD bisects ∠B and ∠D.