On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn. Prove that :
(i) `angle CAD = angle BAE`
(ii) CD = BE

On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn. Prove that : angleCAD=angleBAE

Equilateral triangles ABD and ACE are drawn on sides AB and AC respectively of a DeltaABC outside it. Prove that : (i) angleDAC= angleEAB (ii) DC = BE

The sides AB and AC of a triangle ABC are produced, and the bisectors of the external angles at B and C meet at P. Prove that if AB gt AC , then PC gt PB .

The given figure shows a parallelogram ABCD. Squares ABPQ and ADRS are drawn on sides AB and AD of the parallelogram ABCD. Prove that : (i) angle SAQ = angle ABC (ii) SQ = AC

In the following figure, ABC is an equilateral triangle and P is any point in AC, prove that : (i) BP gt PA (ii) BP gt PC

In the following figure, ABC is an equilateral triangle and P is any point in AC, prove that : (i) BP gt PA (ii) BP gt PC

The P lies on side AB of an equilateral triangle ABC. Arrange AC, AP and CP in descending order.

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

The angles A, B and C of a triangle ABC are in arithmetic progression. AB=6 and BC=7. Then AC is :

In the figure given alongside, squares ABDE and AFGC are drawn on the side AB and the hypotenuse AC of the right triangle ABC. If BH perpendicular to FG, prove that : (i) DeltaEAC~=DeltaBAF . (ii) Area of the square ABDE = Area of the rectangle ARHF.