ABC is a triangle, right angled at B. If BCDE is a square on side BC and ACFG is a square on AC, prove that AD = BF.

ABC is a triangle right angled at C. If AB=25cm and AC=7cm, find BC.

ABC is a right triangle right angled at A. BCED, ACFG and ABMN aresquares on the sides BC, CA and AB respectively. Line segment A X_|_D E meets BCat Y. Show that:(i) DeltaM B C~=DeltaA B D (ii) a r\ (B Y X D)\ =\ 2\

ABC is a right angled triangle with ABC = 90^@ . D is any point on AB and DE is perpendicular to AC. Prove that: If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.

ABC is a right angled triangle with ABC = 90^@ . D is any point on AB and DE is perpendicular to AC. Prove that: DeltaADE~DeltaACB .

ABC is a right triangle right-angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^2+ CD^2= AC^2+ DE^2

In a triangle ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that : AD = CE.

In Fig. 3, ABC is a right triangle, right angled at C and D is the mid-point of BC. Prove that AB^2 = 4AD^2 - 3AC^2 .

In the adjoining figure, ABC is a triangle right-angled at vertex A and AD is altitude. Prove that : Delta ABD is similar to DeltaCAD .

ABC is a triangle, right angled at B, M is a point on BC. Prove that : AM^(2) + BC^(2) = AC^(2) + BM^(2)

A Delta ABC is right angled at A. L is a point on BC such that AL bot BC. Prove that /_BAL = /_ACB .