Show that each diagonal of a rhombus bisects the angle through which it passes:

Isaias Black

Isaias Black

Answered question

2023-01-22

Show that each diagonal of a rhombus bisects the angle through which it passes: ?

Answer & Explanation

Digngoorpr43

Digngoorpr43

Beginner2023-01-23Added 14 answers

Step 1
In rhombus ABCD, AC is its diagonal we have to prove that AC bisects ∠A and ∠C.
A Now, in ΔABC and ΔADC
AC = AC (Common)
AB = CD (Sides of a rhombus)
BC=AD
∴ΔABC≅ΔADC (SSS condition)
∴∠BAC=∠DAC and ∠BCA=∠DCA (c.p.c.t.)
Step 2
So AC bisects the angle A.
Similarly, by joining BD, we can prove that BD bisects ∠B and ∠D.
As a result, each rhombus diagonal bisects the angle through which it passes.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Elementary geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?