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

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)

If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x+y=1, then orthocentre of the triangle is :

Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 2/3 of a right angle.

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.

If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a right triangle with the angle opposite the first sides as right angle.

In the given triangle, name the following: (a). The vertices of the triangle (b). The sides of the triangle (c) the side opposite to vertex Q (d) the vertex opposite to side PQ (e) the three angles using three letters (f) the three angles using a single letter

Two sides of a triangle are of lengths sqrt6 and 4 and the angle opposite to smaller side is 30. How many such triangles are possible? Find the length of their third side and area.

Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite to the shorter side of the two is pi/4 . The largest possible length of the third side is

If two sides of a triangle are unequal, the longer side has greater angle opposite to it. GIVEN : A A B C in which A C > A Bdot TO PROVE : /_A B C >/_A C B CONSTRUCTION : Mark a point D on A C such that A B=A Ddot Joint B Ddot