Fill in the blanks to make the following statements true: In a right triangle the hypotenuse is the ...... side. The sum of three altitudes of a triangle is ......... than its perimeter. The sum of any two sides of a triangle is ......... than the third side. If two angles of a triangle are unequal, then the smaller angle has the ........... side opposite to it. Difference of any two sides of a triangle is ......... than the third side. If two sides of a triangle are unequal, then the larger side has ..... angle opposite to it.

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

Theorem 7.8 : The sum of any two sides of a triangle is greater than the third side.

Show that in a right angled triangle, the hypotenuse is the longest side.

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.

Theorem 7.6 : If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater)

Show that the difference of any two sides of a triangle is less than the third side. GIVEN : triangle A B C TO PROVE : (i) AC-AB < BC

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.

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

In a triangle the greater angle has the longer side opposite to it.