ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that
(i) `DeltaAPB ~= DeltaCQD`
(ii) `AP = CQ`

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP= BQ (see the given figure) Show that: DeltaAQB ~= DeltaCPD

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP= BQ (see the given figure) Show that: DeltaAPD ~= DeltaCQB

Ray 1 is the bisector of an angle angle A and B is any point on I. BP and BQ are perpendiculars from B to the arms of angle A (see the given figure). Show that: (i) triangleAPB=triangleAQB (ii) BP = BQ or B is equidistant from the arms of angleA

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP= BQ (see the given figure) Show that: AP= CQ

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 .

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

In Delta^(s)ABC and, AB"||"DE, BC=EF and BC"||"EF . Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that (i) ABED is a parallelogram (ii) BCFE is a parallelogram (iii) AC = DF (iv) DeltaABC~=DeltaDEF

P is a point equidistant from two lines l and m intersecting at point A (see figure). Show that the line AP bisects the angle between them.

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

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