Are there vestigial organs in plants?

Yes, the Spring on the ends of the Bud scales of maple see small leaves - it vestiges of true leaves. The rhizomes of couch grass, Lily of the valley, fern, plants, aspidistra have scales - rudimentary leaves. In the marginal flowers of the inflorescence of leucanthemum, asters, marigolds, sunflowers and many other Asteraceae under a magnifying glass well-marked immature stamens and pistils. Staminate flowers have a cucumber in the centre of the mound — the rest of the pistil.
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