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

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

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

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

If the two sides of a triangle of a triangle and the included angle are given by a= sqrt(3)+1, b = 2 and C = 60^(@) , find the other two angles and the third side.

If A B C and D E F are similar triangles such that 2\ A B=D E and B C=8c m , then E 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.

If Delta A B C ~ Delta D E F such that B C=3c m , E F=4c m and a r( A B C)=54 c m^2 , then a r( D E F)=

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 .

The bisectors of the angles B and C of a triangle A B C , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.