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??ADB??BFP，? ?AB?BP，??A??FBP，??△ABD≌△BPF． ?BD?PF． ?BD?DE．
30. 解：（1）略.
（2）证明：∵BC=BD，点E是BC的中点，点F是BD的中点， ∴BE=BF.又∠ABC=∠ABD，AB=AB，∴△ABE≌△ABF. 31. （１）如图：
（２）证明△BCD≌△EAD即可.
32. 解：（1）图中共有5个三角形； ·········································· （2分）
AE． · （2）△CGF≌△G··············································· （3分）
∵ △ABC是等边三角形，∴ ∠A?∠C．························ （4分）
∵ E、F、G是边AB、BC、AC的中点， ∴AE=AG=CG=CF=
12AB． ····································································· （6分）
AE． ·∴ △CGF≌△G··········································································· （7分）
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