The parallelogram ABCD is known. The straight line FH intersects AB and CD. Through a, B, C and D, the perpendicular lines of FH are made. The perpendicular feet are e, h, G and F. verification: ae-df = cg-bh

The parallelogram ABCD is known. The straight line FH intersects AB and CD. Through a, B, C and D, the perpendicular lines of FH are made. The perpendicular feet are e, h, G and F. verification: ae-df = cg-bh

∠FDC＝∠ EAB.DF +GC＝DCcos∠FDC＝ABcos∠EAB＝AE+HB,AE-DF=CG-BH

Given that the line L passes through the vertex B, AA '⊥ L, CC' ⊥ L, DD '⊥ l of the parallelogram ABCD, it is proved that AA' + CC '= DD'
Given that line L passes through vertex B, AA & # 39; ⊥ L, CC & # 39; ⊥ L, DD & # 39; ⊥ l of parallelogram ABCD, prove AA & # 39; + CC & # 39; = DD & # 39;

The auxiliary line am is perpendicular to dd'm, because am is perpendicular to DD ', BD' is perpendicular to DD ', so am / / BD', and because AD / / BC, ad = BC, so angle dam = CBD ', so triangle dam is equal to triangle CBD', so DM = CC '