AX and DY are altitudes of two similar triangles `Delta ABC and Delta DEF`. Prove that AX : DY = AB : DE.

Define : Similar triangles

In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

Given that Delta ABC ~ Delta PQR , CM and RN are respectively the medians of Delta ABC and Delta PQR . Prove that (i) Delta AMC ~ Delta PNR (ii) (CM)/(RN) = (AB)/(PQ) (iii) Delta CMB ~ Delta RNQ

If the areas of two similar triangles are equal, prove that they are congruent.

AD, BE and CF are altitudes of triangle ABC. If AD = BE = CF, prove that triangle ABC is an equilateral triangle.

Delta ABC and Delta AMP are two right triangles right angled at B and M respectively. Prove that (i) Delta ABC ~ Delta AMP and (ii) (CA)/(PA) = (BC)/(MP) .

In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt AD.

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

In triangle ABC, AD, BE and CF are altitudes. Prove I, that, AD + BE + CF lt AB + BC + CA