Question

In the parallelogram abcd, the angles a and c are obtuse. points x and y are taken on diagonal bd such that xad and ycb are rt. angles prove=xa=yc

Answer 1

Given : ABCD is a parallelogram and AX and CY are perpendicular on diagonal BD Now In ∆ABX and ∆CDY ⇒ ∠AXB = ∠CDY = 90° (Given) and ∠ABX = ∠CDY (Alternate opposite angles) AB = CD (opposite sides of a ||gm) ∆ABX ≅ ∆CDY (by AAS congruency criterion) ⇒ AX = CY

Answer 2

in //gm abcd

angle ADC = angle ABC (opp angles of //gm )

diagonal BD bisects angle B and angle C

<ABD=<DBC=<BDA=<CDB

in triangle AXD and triangle BCY

BC= AD ( Opp side of//gm)

<XAD=<BCY= 90°

<XDA=<YBC (Proved above)

thus

triangle AXDis congruent to triangleBCY ( ASA )

XA=YC (CPCTC)

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