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Question
If the median drawn on the base of a triangle is half its base, the triangle will be:
Options
right-angled
acute-angled
obtuse-angled
equilateral
MCQ
Solution
right-angled
Explanation:
I ∼ ΔABC, Let BC = x
Since AD is the median,
∴ BD = DC = `x/2`
Also AD = `1/2` BC = `1/2 x` or `x/2`
In ΔABD, AD = BD
Similarly in ΔADC, ∠DAC = ∠ACD,
∠A = a + b
Thus, a + b + a + b = 180°
⇒ a + b = 90°
⇒ ∠A = 90°
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Geometry (Entrance Exam)
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