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 A B C in which A D ,B E and C F are its medians. TO PROVE : A B+B C+A C > A D+B E+C F

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

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

Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

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

Which of the following statements are true (T) and which are false (F)? (i) Sum of the three sides of a triangle is less than the sum of its three altitudes. (ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side. (iii) Sum of any two sides of a triangle is greater than the third side. (iv) Difference of any two sides of a triangle is equal to the third side. (v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. (vi) 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.

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle.

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle.

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. GIVEN :triangle A B C in which A D_|_B C ,B E_|_A C and C F_|_A Bdot PROVE : A D+B E+C F < A B+B C+A C

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.