题目

For the first time, researchers have discovered that some plants can kill insects in order to get additional nutrients. New research shows that they catch and kill small insects with their own sticky hairs near the roots and then absorb nutrients through their roots when the insects are killed and fall to the ground. Professor Mark Chase, of Kew and Queen Mary, University of London, said: “The cultivated (改良的) tomatoes and potatoes still have the hairs. Tomatoes in particular are covered with these sticky hairs. They do trap small insects on a regular basis. They do kill insect如图，四边形ABCD中，AB∥CD，AC平分∠BAD，CE∥AD交AB于E．（1）求证：四边形AECD是菱形；（2）若点E是AB的中点，试判断△ABC的形状，并说明理由．