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Equal Intercept Theorem

In the given ...

Question

In the given $Δ$ ABC, M and N are mid-points of AB and AC respectively. D is any point on the base BC. Which of the following relationships will always hold true?

ME = EN

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BD = DC

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AE = ED

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A D = \frac{1}{2} A B

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Solution

The correct option is C AE = ED
Look at the figure carefully.
Since M & N are mid - points of AB & AC, MN || BC (according to mid - point theorem).
$\Rightarrow$ Now, consider AB, AD, AC. They all act like a transversal.
$∴$ By equal intercept theorem, AE = ED.

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In the given Δ ABC, M and N are mid-points of AB and AC respectively. D is any point on the base BC. Which of the following relationships will always hold true?

The correct option is C AE = EDLook at the figure carefully. Since M & N are mid - points of AB & AC, MN || BC (according to mid - point theorem). ⇒ Now, consider AB, AD, AC. They all act like a transversal. ∴ By equal intercept theorem, AE = ED.

In the given $Δ$ ABC, M and N are mid-points of AB and AC respectively. D is any point on the base BC. Which of the following relationships will always hold true?

The correct option is C AE = ED
Look at the figure carefully.
Since M & N are mid - points of AB & AC, MN || BC (according to mid - point theorem).
$\Rightarrow$ Now, consider AB, AD, AC. They all act like a transversal.
$∴$ By equal intercept theorem, AE = ED.