Question

PROVE THAT
Two triangles on the same base and between the same parallels are equal in area.​

Answer 1

Answer:

Step-by-step explanation:

theorem: Two triangles on the same base and between the same parallels are equal in area.

Given: ABCD is a parallelogram in which AC is diagonal.

To Prove: ar(ADC) = ar(ABC)

Construction: draw AN perpendicular to DC and CF perpendicular to AB

Proof: consider triangles ADN and CBF

AD= BC------opp. sides of parallelogram are equal

angle ADN = angleCBF------- opp. angles of parallelogram are equal

angle AND = angleCFB

so, triangles are congruent by AAS criterion

now,

AN = CF (CPCT)

NOW,

AR(ADC) = 1/2 × DC × AN

AR(CBA) = 1/2 × AB × CF

AS WE KNOW AN AND CF ARE EQUAL

AND AB = DC-------------opposite sides of parallelogram are equal

AR(ADC) = AR(CBA)

HENCE PROVED.

HEY BRO DIFFERENT INSTITUITIONS USE DIFFERENT METHODS TO SOLVE THIS ...U CAN CHOOSE THE ONE WHICH FEELS EASIER FOR U........

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Step-by-step explanation: