Question

i selected the answer i thought was right
but if i'm wrong please correct me

Answer 1

Answer:

angle(ADB)=angle(CBD)

ADC+DCB=180

AE=CE

Step-by-step explanation:

we will verify each options

option-A:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

and alternate interior angles are always equal

so,

angle(ADB)=angle(CBD)

so, this is TRUE

option-B:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

so, we get

ADC+DCB=180

so, this is TRUE

option-C:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

$angle(DEC)\neq angle(DEA)$

so, this is FALSE

option-D:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

so, this is TRUE

option-E:

Since, AC and DB are diagonals of parallelogram

so, they can not be equal

so, this is FALSE