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

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

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

In two triangles A B C\ a n d\ D E F , it is given that /_A=/_D ,\ /_B=/_E and /_C=/_Fdot Are the two triangles necessarily congruent?

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

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.

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 .

D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

The sides B C ,C A and A B of a triangle A B C , are produced in order, forming exterior angles /_A C D ,/_B A E and /_C B F . Show that /_A C D+/_B A E+/_C B F=360^0

The sides B C ,C A and A B of a triangle A B C , are produced in order, forming exterior angles /_A C D ,/_B A E and /_C B F . Show that /_A C D+/_B A E+/_C B F=360^0