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Side by side
What tells them apart
Both have compound leaves and winged fruit. Ash has leaflets toothed along the whole margin and black buds in winter; tree of heaven has smooth-edged leaflets with two glandular teeth at the base, and smells bad.
Harmless confusion
How to tell it
A huge compound leaf with fifteen to thirty leaflets, and the decisive sign is at each leaflet's base: one or two coarse teeth with a gland at the tip, which no other native tree has. Crushed, the leaf smells bad, like rancid butter. Winged fruits in reddish clusters.
How to tell it
A leaf divided into several narrow toothed leaflets, opposite along an axis. Black velvety buds in winter. Winged fruits in bunches that stay on after leaf fall.