Cockroaches and other members of the order Blattodea have wings.
Above their abdomens are two pair of leathery, scleritized (hardened) wings.
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Earwigs, the insects that make up the Dermaptera order have very
small, skin-like flaps for their forwings (hense the name dermapter, skin-wing)
which cover the folded-up hind wings.
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True bugs (hemipterans) have leathery tegmina as forwings that
cross over their membranous hind wings and backs. These count as
wings also.
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Praying Mantises and related mantodea also have wings. The
forwings have been modified into long, partially hardened protective layers
to cover the membranous hind wings.
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Butterflies and moths, the insects that make up the lepidoptera
family have very noticeably, often brightly colored, scale-covered wings.
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Grasshoppers, katydids, crickets and other orthopterans have wings
that work in much the same way as mantises. The front wing is ridgid
and protects the membranous hind wing.
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