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

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

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side. GIVEN : triangle A B C in which A D is a median. PROVE : A B+A C >2A D CONSTRUCTION : Produce A D to E such that A D=D E . Join E C .

Two triangles are congruent if include 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 triangle A B C and D E F such that /_B=/_E ,/_C=/_F and B C=E F TO PROVE : triangle A B C~=triangle D E F

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

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

In figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC . If A D_|_B C and E F_|_A C , prove that DeltaA B D ~DeltaE C F .

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.

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.