Theorem 6.2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

If two sides of a triangle are hati+2hatj and hati+hatk , then find the length of the third side.

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.

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

Using Theorem 6.2, prove that the line joining the mid-point of any two sides of a triangle is parallel to the third side. (Recall that you have done it in class IX).

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

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

If two side of a triangle are hat i+2 hat j and hat i+ hat k , then find the length of the third side.

Prove that the line joining the mid-points of the two sides of a triangle is parallel to 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.

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