Math, asked by chickenpoxisbad, 4 months ago

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.

God will bless you if you answer the question with the full process. I will give brainliest to the one who answers with the full process.

Answers

Answered by dolemagar
1

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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