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 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 right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

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.

Two equal sides of a triangle are each 5 metres less than twice the third side. If the perimeter of the triangle is 55 meters, find the lengths of its sides.

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

Prove that the altitudes of a triangle are concurrent.

Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

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