Question

challenge to brainly solvethis​

Answer 1

Angle A + Angle B = 180 (CO-INTERIOR ANGLES)

ANGLE B = 180 - ANGLE A

NOW,

IN ABP

ANGLE APB + ANGLE BAP + ANGLE ABP = 180 ( ANGLE SUM PROP. OF TRIANGLE)

I'M WRITING AN SHORT FOR ANGLE-

AN B +1/2 AN A + AN APB = 180

180 - AN A + 1/2 AN A + AN APB = 180

AN APB = AN A -1/2 AN A

AN B = 1/2 AN A

AN B = AN BAP

THEREFORE

AB = BP

( SIDES OPPOSITE TO EQUAL ANGLES ARE EQUAL IN LENGTH)

MULTIPLYING BOTH SIDES BY 2

2 AB = 2 BP

2 AB = BC

2 CD = AD

( SINCE AB = CD AND BC = AD OPPOSITE SIDES OF PARALLELOGRAM ARE EQUAL)

HENCE PROVED

Answer 2

Answer:

Angle A + Angle B = 180 (CO-INTERIOR ANGLES)

ANGLE B = 180 - ANGLE A

NOW,

IN ABP

ANGLE APB + ANGLE BAP + ANGLE ABP = 180 ( ANGLE SUM PROP. OF TRIANGLE)

I'M WRITING AN SHORT FOR ANGLE-

AN B +1/2 AN A + AN APB = 180

180 - AN A + 1/2 AN A + AN APB = 180

AN APB = AN A -1/2 AN A

AN B = 1/2 AN A

AN B = AN BAP

THEREFORE

AB = BP

( SIDES OPPOSITE TO EQUAL ANGLES ARE EQUAL IN LENGTH)

MULTIPLYING BOTH SIDES BY 2

2 AB = 2 BP

2 AB = BC

2 CD = AD

( SINCE AB = CD AND BC = AD OPPOSITE SIDES OF PARALLELOGRAM ARE EQUAL)

HENCE PROVED.................................

Step-by-step explanation: