Question

The vertex A of angle ABC is joined to point D on side BC and E is the midpoint of side Ad

Prove that: ar(BEC) = 1/2 ar (ABC)

Answer 1

Answer:

From the figure we know that BE is the median of △ ABD So we get Area of △ BDE = Area of △ ABE It can be written as Area of △ BDE = ½ (Area of △ ABD) …… (1) From the figure we know that CE is the median of △ ADC So we get Area of △ CDE = Area of △ ACE It can be written as Area of △ CDE = ½ (Area of △ ACD) …….. (2) By adding both the equations Area of △ BDE + Area of △ CDE = ½ (Area of △ ABD) + ½ (Area of △ ACD) By taking ½ as common Area of △ BEC = ½ (Area of △ ABD + Area of △ ACD) So we get Area of △ BEC = ½ (Area of △ ABC) Therefore, it is proved that ar (△ BEC) = ½ ar (△ ABC)

Answer 2

Step-by-step explanation:

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