Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. GIVEN : A ` A B C` in which `A D_|_B C ,B E_|_A C` and `C F_|_A Bdot` PROVE : `A D+B E+C F

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. GIVEN :triangle A B C in which A D_|_B C ,B E_|_A C and C F_|_A Bdot PROVE : A D+B E+C F < A B+B C+A C

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

In Figure, A B_|_B C ,F G_|_B C and D E_|_AC.Prove that triangle A D E~G C F

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

Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle. GIVE : Two s A B C and D E F such that /_B=/_E ,/_C=/_F and B C=E F TO PROVE : A B C~=D E F

Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other triangle. GIVEN : Two triangles A B C and D E F such that A B=D E ,A C=D F and /_A=/_D PROVE : A B C~= D E F Figure

The sum of any two sides of a triangle is greater than the third side. GIVE : A triangle A B C TO PROVE : A B+A C > B C ,A B+B C > A C and B C+A C > A B CONSTRUCTION : Produce side B A to D such that A D=A Cdot Join C D .

If any two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the two triangles are congruent. GIVEN : Two s A B C and D E F such that /_A=/_D ,/_B=/_E ,B C=E F TO PROVE : A B C~=D E F Figure

If any two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the two triangles are congruent. GIVEN : Two s A B C and D E F such that /_A=/_D ,/_B=/_E ,B C=E F TO TROVE : A B C~=D E F Figure

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.