ABCD is a quadrilateral in which AD=BC and `angleDAB = angleCBA`. Prove that:
(i) `triangleABD ~= triangleBAC`
(ii) BD = AC
(iii) `angleABD = angleBAC`

ABCD is a quadrilateral in which AD = BC and /_ DAB = /_ CBA Prove that (i) DeltaABD ~= DeltaBAC (ii) BD = AC (iii) /_ ABD = /_ BAC

ABCD is a quadrilateral. Is AB+BC+CD+DA>AC+BD?

triangleABC and triangleDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that: (i) triangleABD ~= triangleACD (ii) triangleABP ~= triangleACP (iii) AP bisects angleA as well as angleD (iv) AP is the perpendicular bisector of BC.

ABCD is a trapezium in which AB abs CD and AD = BC. Show that diagonal AC = diagonal BD

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that (i) DeltaABD ~= DeltaACE (ii) AB = AC i.e., ABC is an isosceles triangle.

In the adjacent figure, it is given that AB =AC, angleBAC = 36^(@) , angleADB = 45^(@) and angleAEC = 40^(@) . Find (i) angleABC (ii) angleACB (iii) angleDAB (iv) angleEAC .

ABCD is a trapezium in which AB||CD and AD=BC Show that angleA=angleB angleC=angleD DeltaABC approx DeltaBAD diagonal AC=diagonal BD

A quadrilateral ABCD is drawn to circumscribe a circle as shown. Prove that AB+CD=AD +BC.

ABCD is a quadrilateral in which P, Q, R and S are mid- points of the sides AB, BC, CD and DA. AC is a diagonal. Show that : PQ=SR