In `triangleABC , angleA= 60^(@)` prove that `BC^(2)= AB^(2)+AC^(2)- AB . AC`

In a quadrilateral ABCD angle B = angle D = 90 ^(@) Prove that : 2AC^(2) - BC^(2) = AB^(2) + AD^(2) +DC^(2)

In a quadrilateral ABCD, angleA+angleD=90^(@) . Prove that AC^(2)+BD^(2)=AD^(2)+BC^(2)

In a quadrilateral ABCD, angleB=90^(@) and angleD=90^(@) . Prove that : " "2AC^(2)-AB^(2)=BC^(2)+CD^(2)+DA^(2)

In the given figure if angleB= 90^(@) and BD is perpendicular to AC then prove that: (i) triangleADB~triangleBDC (ii) triangleADB~triangleABC (iii) triangleBDC ~ triangleABC (iv) BD^(2)= AD xx DC (v) AB^(2)= AD xx AC (vi) BC^(2)= CD xx AC (vii) AB^(2)+BC^(2)= AC^(2)

In a rectangle ABCD, prove that : AC^(2)+BD^(2)=AB^(2)+BC^(2)+CD^(2)+DA^(2) .

In a rhombus ABCD, prove that AC^(2) + BD^(2) = 4AB^(2)

In an acute angled triangle ABC, AD is the median in it. Prove that : AD^(2) = (AB^(2))/2 + (AC^(2))/2 - (BC^(2))/4

In triangleABC, AB=10cm, angleA=45^(@) and angleC=60^(@) . Find BC.

triangleABC is an isosceles triangle with AC = BC. If AB^(2)= 2AC^(2) . Prove that triangle ABC is a right triangle.

In any triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + BD^2) , where D is the midpoint of BC.