Question

In the figure E is any point on median AD of a Triangle ABC Show that ar (ABE)=ar (ACE)​

Answer 1

hey!!

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Given:-

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AD is a median of ABC and E is any point on AD.

To prove :

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• ar (ABE) = ar (ACE)

Proof :

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AD is the median of ABC

• ar (ABD) = ar (ACD) ...(1)

• aED is median of EBC
• ar (BED) = ar (CED) ...(2)

Subtracting (2) from (1)

• ar (ABD) – ar (BED) = ar (ACD) – ar (CED)

• ar (ABD) – ar (BED) = ar (ACD) – ar (CED) ar (ABC) = ar (ACE).

• ar (ABD) – ar (BED) = ar (ACD) – ar (CED) ar (ABC) = ar (ACE).Hence Proved.

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hope help u!!

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Answer 2

Hello ☺

Given :

AD is a median of ABC and E is any point on AD.

To prove :

ar (ABE) = ar (ACE)

Proof :

AD is the median of ABC

ar (ABD) = ar (ACD) ...(1)

aED is median of EBC

ar (BED) = ar (CED) ...(2)

Subtracting (2) from (1)

ar (ABD) – ar (BED) = ar (ACD) – ar (CED)

ar (ABC) = ar (ACE).

Hence Proved.

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