In ΔABC, AD is the median and G is the Centroid. AG : AD = ?
1 : 3
2 : 3
1 : 4
1 : 2
Centroid divides median in the ratio 2 : 1.
AG : GD = 2 : 1 [Step 1.]
AG : AD = 2 : 3 [Since AD = AG + GD = 2GD + GD = 3GD.]
Correct answer : (2)
In what type of triangle at least one median coincides with an altitude?
either isosceles or equilateral
In an isosceles triangle, the median from the vertex containing the congruent sides is perpendicular to the base.
In an equilateral triangle, the median from any vertex to the opposite side will be perpendicular to that side.
So, in isosceles triangle and equilateral triangle, at least one median coincides with an altitude.
Correct answer : (1)
Select the correct statement/statements. 1. In an equilateral triangle, orthocenter coincides with incenter. 2. In an equilateral triangle, median and angle bisector from a vertex are the same. 3. In an equilateral triangle, centroid coincides with circumcenter.
1, 2, and 3
In an equilateral triangle, median, altitude, perpendicular bisector and angle bisectors are same.
So, centroid, orthocenter, incenter and circumcenter of an equilateral triangle coincide.