Question

ABCD is a rhombus. AC and BD are the diagonals intersecting each other at O. Show that ∆AOD ≌ ∆COD

Answer 1

Step-by-step explanation:

OA = OC and OB = OD [given]

In triangle AOD and triangle COD

AO = OC [ GIVEN ]

∠AOD = ∠COD [ VERTICALLY OPPOSITE ANGLES]

BO = OD [ GIVEN ]

So, triangle AOD is congruent to triangle COD [ SAS ]

Answer 2

Step-by-step explanation:

We know that , diagonals of rhombus bisect each other.

So, OA = OC and OB = OD [given]

In triangle AOB and triangle COD

AO = OC [ GIVEN ]

∠AOB = ∠COD [ VERTICALLY OPPOSITE ANGLES]

BO = OD [ GIVEN ]

So, triangle AOB is congruent to triangle COD [ SAS ]