If the median of a triangle passes through the opposite side at a 90° angle, then the triangle is equilateral. Is this statement true always, sometimes or never? Explain and justify your answer.
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Step-by-step explanation:
Ok dude, The answer is sometimes true.
Firstly median is the midpoint of the opposite side,
Now let's consider 2 points( A and B) on a blank sheet, take a mid point (D), now connect AB, you have a straight line now. From D, draw a perpendicular line and name it C. Now connect AC and BC, you'll notice that you have two similar triangles ∆ ADC and ∆BDC
such that AD= BD (midpoint of AB)
DC=DC (common side)
L ADC= L BDC= 90°
Thus, you've proved ∆ADC≈∆BDC
hence, AC= BC (corresponding sides)
So, in∆ABC , AC=BC
but that does not prove that AC= AB
all equilateral triangles are isosceles but all isosceles ∆`s are not equilateral.
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