Q: Which shows a median constructed to side AB of ABC?

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Two. However, you can actually do it with just one. Consider the median AD of triangle ABC. Then the point G, 2/3 of the way from A to D, is the centroid. This process (2/3 of the way from the vertex to the opposite side) can be applied to any median.

Let the triangle be ABC and suppose the median AD is also an altitude.AD is a median, therefore BD = CDAD is an altitude, therefore angle ADB = angle ADC = 90 degreesThen, in triangles ABD and ACD,AD is common,angle ADB = angle ADCand BD = CDTherefore the two triangles are congruent (SAS).And therefore AB = AC, that is, the triangle is isosceles.

No.

It depends on whether you mean median in terms of statistical data or the line joining a vertex of a triangle to the midpoint of the opposite side. The Statistical Median: If there are n observations where n is odd, then the median is the (n+1)/2 smallest observation. If n is even, then the median is the arithmetical mean of the n/2 and n/2+1 smallest observations. The Coordinate Geometry Median: Given triangle ABC, with A = (xa, ya), B = (xb, yb) and C = (xc, yc), the midpoint, D of BC is [(xb+xc)/2, (yb+yc)/2] and so, the equation of the median AD is (y-ya)/(x-xa) = (2ya-yb-yc)/(2xa-xb-xc)

Any side: you can select the order in which the vertices are named!

Related questions

Isosceles

It is isosceles.

It is isosceles.

It is a median.

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Two. However, you can actually do it with just one. Consider the median AD of triangle ABC. Then the point G, 2/3 of the way from A to D, is the centroid. This process (2/3 of the way from the vertex to the opposite side) can be applied to any median.

ABC family shows over 50 shows but switched at birth is like an angel to my ears!

Let the triangle be ABC and suppose the median AD is also an altitude.AD is a median, therefore BD = CDAD is an altitude, therefore angle ADB = angle ADC = 90 degreesThen, in triangles ABD and ACD,AD is common,angle ADB = angle ADCand BD = CDTherefore the two triangles are congruent (SAS).And therefore AB = AC, that is, the triangle is isosceles.