Line AB and CD are intersecting at ‘O’, OA = OB and OD = OC. Show that (i) `Delta AOD ~= DeltaBOC` and (ii) `AD || BC`.

Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD. Show that (i) DeltaAOB ~= DeltaDOC (ii) O is also the mid-point of BC.

In the given figure, AB||DC and AD||BC show that DeltaABC ~= Delta CDA .

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.

Two sides AB, BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of DeltaPQR . Show that: (i) DeltaABM ~= DeltaPQN (ii) DeltaABC ~= DeltaPQR

In an isosceles triangle ABC, with AB = AC, the bisectors of /_ B and /_ C intersect each other at O. Join A to O. Show that : (i) OB = OC (ii) AO bisects /_A

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

In quadrilateral ABCD, AB = CD, BC=AD show that DeltaABC ~= DeltaCDA Consider DeltaABC and DeltaCDA

ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and Parallel to BC intersects AC at D. Show that (i) D is the midpoint of AC (ii) MD_|_AC (iii) CM=MA=(1)/(2)AB.

In right triangle ABC, right angle is at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see figure). Show that : (i) DeltaAMC ~= DeltaBMD (ii) /_DBC is a right angle (iii) Delta DBC ~= DeltaACB (iv) CM = 1/2 AB .

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD "||" BA as shown in the figure. Show that (i) angleDAC = angleBCA (ii) ABCD is a parallelogram