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

Prove that the sum of the three angles of a triangle is 180^0dot

If the altitudes of a triangle are in A.P,then the sides of the triangle are in

Show that the difference of any two sides of a triangle is less than the third side.

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.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Show that the altitudes of a triangle are concurrent

We know that the sum of the interior angles of a triangle is 180^0 . Show that the sums of the interior angles of polygons with 3,4,5,6 sides form an arithmetic progression. Find the sum of the interior angles of a 21 sided polygon.

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