Question

(Figure 1) In the parallelogram ABCD,AD=2AB,a point M is mid- point of segment AD,CE⊥AB,if∠CEM=40°,then the value of∠DME it(  ).

    (A)150°    (B)140°    (C)135°    (D)130°

Answer 1

如圖,連接CM,作MN⊥EC于N.

    ∵ AB⊥CE  ∴MN∥AB,且MN∥CD,從N為梯形AECD的中位數.

    由MN⊥CE,MN是EC邊中線,∴△EMC為等腰△,

    ∴∠ECM=∠MEC=40°　∠EMC=180°-2×40°=100°

    ∵ ∠ECD=∠AEC=90°,∴∠MCD=90°-40°=50°,

    又∵ DC=AD=DM,∴∠MCD=∠DMC=50°,∴

    ∠EMD=∠EMC+∠CMD=100°+50°=150°.選(A)