Praying Mantis or Preying Mantis (both work as a descriptive) are in the Order Mantodea - Family of Mantidae. Mantis is a Greek word meaning prophet or soothsayer. Mantis is the singular form of the word and the plural form is Mantids. In English we commonly call them Praying Mantis because of the typical pose of the front legs folded up to look like praying hands. In Israel one of the words used for a Mantis means Mohammad’s camel.
Praying Mantis feed on other insects, spiders and each other. They are true cannibals and often the little ones will eat each other to establish a territory. They also eat other predatory insects so can not be trusted to leave the other good guys alone. Here in the US at least 20 different species of Mantids have been identified living in North America. They are usually green or beige in color.
Eggs are laid in the fall so you may find egg cases stuck to garden structures, fences, eaves and branches. Eggs will overwinter and hatch In the spring. Leave them be so that you will have the advantage of the little predators hatching out in the spring to go after other insects in the yard. The adults generally live from spring to late Autumn. The egg cases here in the Vegas Valley look different than most of the ones that are seen in other parts of the world or mentioned in books.