Saved Bookmarks
| 1. |
Don AC, prove thĂĽt XbShow that the quadrilateral formed by joining the mid-points of the sides of a squareis also a square. |
|
Answer» Let a square ABCD in which L,M,N&O are the midpoints . in triangle AML and triangle CNO AM = CN ( AB = DC and M and O are the midpoints ) AL = CM ( AD = BC and L and N are the midpoints ) angle MAL = angle NCO ( all angles of a square = 90 degree ) by AAS critaria triangle AML CONGRUENT totriangle CNO therefore ML = ON ( CPCT )similarly in triangle MBN CONGRUENT toLDO and AND triangle AML is CONGRUENT to trianglenow , in Triangle AML ,angle AML = angle ALM ( AM = AL ) = 45 degree similarly in triangle LDO angle DLO = 45 degreethere fore ,angle MLO = 90 degree by the properties of SQUAREall sides are equal and angles are 90 degree |
|