Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) Delta AOB cong Delta DOC (ii) O is also the mid-point of BC.

In Fig. 6.37, if Delta ABE~=Delta ACD , show that Delta ADE~Delta ABC .

In Fig, OA . OB = OC . OD. Show that angle A=angle C and anlge B=angleD .

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB (see Fig. 8.14). Show that (i) angle DAC = angle BCA and (ii) ABCD is a parallelogram.

In Fig. 7.21, AC = AE, AB = AD and angle BAD = angle EAC . Show that BC =DE.

ABCD is a quadrilateral in which AD = BC and angle DAB =angle CBA (see Fig. 7.17). Prove that (i) triangle ABD cong triangle BAC (ii) BD = AC (iii) angle ABD = angle BAC .

Line l is the bisector of an angle angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of angle A (see Fig. 7.20). Show that: (i) triangle APB cong triangle AQB (ii) BP = BQ or B is equidistant from the arms of angle A .

In Fig., 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

In quadrilateral ACBD, AC = AD and AB bisects angle A (see Fig. 7.16). Show that triangle ABC cong triangle ABD . What can you say about BC and BD?

In the triangle ABC, lines OA,OB and OC are drawn so that angles OAB, OBC and OCA are each equal to omega , prove that cotomega=cotA+cotB+cotC