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 in which AD = BC and angle DAB = angle CBA (see the given figure). Prove that ( i ) triangle ABD = triangle BAC, ( ii) BD = AC and (iii) angle ABD = angle BAC

In quadrilateral ABCD, BA = BC and DA = DC. Prove that BD bisects angle ABC as well as angle ADC.

In quadrilateral ACBD, AC = AD and AB bisects /_A Show that DeltaABC~= DeltaABD . What can you say about BC and BD?

ABC is a Deltain which /_B lt 90^(@)" and "AD bot CB . Prove that AC^(2)= AB^(2)+BC^(2)-2BC*BD .

In the given figure ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angle DBC = 55 ^(@) and angle BAC = 45 ^(@), find angle BCD.

ABD is a triangle right angled at A and AC bot BD Show that (i) AB^(2) = BC .BD. (ii) AC^(2) = BC.DC (iii) AD^(2) = BD .CD.

ABC is a Deltain which /_B gt 90^(@)" and "AD bot CB produced. Prove that AC^(2)= AB^(2)+BC^(2)+2BC*BD .

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that: ( i ) AD bisects BC ( ii) AD bisects angle A

In a quadrilateral ABCD, /_B= 90^(@)" and "AD^(2)= AB^(2)+BC^(2)+CD^(2) . Prove that /_ACD= 90^(@) .

triangle ABC and triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that, ( i ) triangle ABD = triangle ACD (ii) triangle ABP = triangle ACP (iii) AP bisects angle A as well as angle D. (iv) AP is the perpendicular bisector of BC