如图,点C为线段AB上一点,△ACM,△CBN是等边三角形.

∵ AC = MC ,NC = BC ,∠MCB = ∠ACN = 120°
∴ △ACN ≌ △BCM
∴ AN = BM ,∠ANC = ∠CBM
∴ △CPN ≌ △CQB
∴ CP = CQ ,∠BCQ = ∠NCP
∵ ∠BCQ + ∠QCN = ∠BCN = 60°
∴ ∠NCP + ∠ QCN = ∠PCQ = 60°
∴ △CPQ为等边三角形(60°的等腰三角形)