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In ΔBECΔBEC , DD is a midpoint so EDED is a median.[Math Processing Error]
∴\arBDE=\arCDE(1)(1)∴\arBDE=\arCDE
Now, ΔADEΔADE and ΔBDEΔBDE are on the same base DEDEand between the same parallels DEDE and ABAB.
∴\arADE=\arBDE(2)(2)∴\arADE=\arBDE
From (1)(1) and (2)(2):
\arADE=\arCDE(3)(3)\arADE=\arCDE
i.e. DEDE divides ΔADCΔADC into two parts of equal area.
∴∴ DEDE is a median and EE is the midpoint of AC.AC.
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In ΔBECΔBEC , DD is a midpoint so EDED is a median.[Math Processing Error]
∴\arBDE=\arCDE(1)(1)∴\arBDE=\arCDE
Now, ΔADEΔADE and ΔBDEΔBDE are on the same base DEDEand between the same parallels DEDE and ABAB.
∴\arADE=\arBDE(2)(2)∴\arADE=\arBDE
From (1)(1) and (2)(2):
\arADE=\arCDE(3)(3)\arADE=\arCDE
i.e. DEDE divides ΔADCΔADC into two parts of equal area.
∴∴ DEDE is a median and EE is the midpoint of AC.AC.
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vanshikakamboj1331:
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