Prove that the perimeter of a triangle is greater than the sum of its three medians.

Prove that the perimeter of a triangle is greater than the sum of the three medians. GIVEN: A o+ ABC in which AD,BE and CF are its medians.TO PROVE: AB+BC+AC>AD+BE+CF

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Prove that the perimeter of any triangle is greater than the sum of three altitudes.

Consider the following statements : 1. The perimeter of a triangle is greater than the sum of its three medians. 2. In any triangle ABC, if D is any point on BC, then AB + BC + CA gt 2AD. Which of the above statements is/are correct?

Prove that the sum of three altitudes drawn from the vertices to opposite sides of a triangle is less than the sum of three sides. or Prove that the perimeter of a triangle is greater than the sum of three altitudes drawn from the vertices to opposite of a triangle.

Consider the following statements in respect of any triangle I. The three medians of a triangle divide it into six triangles of equal area. II. The perimeter of a triangle is greater than the sum of the lengths of its three medians. Which of the statements given above is/are correct ?

Prove that the sum of any two sides of a triangle is greater than two times the median of third side.

If the perimeter of a triangle is 6, then its maximum area is

Prove that sum of any two medians of a triangle is greater than the third median.

Which of the following statements are true (T) and which are false (F)? Sum of the three sides of a triangle is less than the sum of its three altitudes. Sum of any two sides of a triangle is greater than twice the median drawn to the third side. Sum of any two sides of a triangle is greater than the third side. Difference of any two sides of a triangle is equal to the third side. If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.