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

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL^(2) + CM)^(2) = 5 BC^(2) .

ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of Delta ABE and Delta ACD

ABC is an isosceles triangle of which AC=BC and AB^(2) = 2AC^(2) . Then value of /_C will be -

DeltaABC is an isosceles triangle in which AB = AC. Show that /_ B = /_ C.

In the given figure ABC is a right triangle and right angled at B such that /_BCA = 2/_BAC. Show that hypotenuse AC = 2BC.

Write down the negation of each of the following compound statements : If triangle ABC is right angled at A , then AB^(2)+AC^(2)=BC^(2) .

ABC is a right angled triangle right angled at B. If P and Q are the mid - points of the sides overline(AB)andoverline(BC) respectively , then show that , 4(AQ^(2)+PC^(2))=5AC^(2) .

Write the converse of each of the following conditional statements : If a traiangle ABC is right - angled at C , then AC^(2)+BC^(2)=AB^(2) .

In an isosceles triangle ABC , angleA =120^@ ,a:b=