Rhodophytes were once phylogenetically linked to cyanobacteria because of similarity in two groups of phycobilliprotein pigments, phycocyanins and phycoerythrins, which the algae use as accessory photosynthetic pigments. Whether these pigments are analogous or homologous in the red algae and cyanobacteria is not certain. But it is possible that at least a billion years ago, an ancestral, heterotrophic eukaryote took up a symbiotic relationship with a cyanobacterium-like prokaryote.
That early ancestral lineage is believed to have given rise to today's Rhodophyta and Green Plants.
Rhodophyta is the sister taxon to Green Plants, and both groups are included in the putatively monophyletic taxon Archaeplastida, formerly known as Plantae.
Remember that the above characters are synapomorphies with respect to the taxa which branched off earlier on the phylogenetic tree.
These same characters are considered to be symplesiomorphies with respect to the green algae and plants considered as a group.
These characters are thus not informative in determining further clades within the green plants.
The synapomorphies of land plants relative to their green algae relatives include:
In land plants, gametophyte and sporophyte look completely different (heteromorphy)
Many green algae exhibit a progression of complexity (e.g., the volvocine line of evolution). This should not be taken to represent a progression towards multicellular land plants. It merely shows that many algae appear to be genetically predisposed to have a division of labor among their cells. But this predisposition could be the reason that multicellular plants eventually did evolve
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Each zygote undergoes meiosis to produce four new haploid propagules, which are released from the cell wall of the former vegetative cell to grow into new, haploid filaments of algae.
The organism's body (a.k.a. thallus; a plant body not differentiated into roots, stems and leaves) consists of large cells that may be several centimeters long. The algae may branch at nodes made up of smaller cells.
As in land plants, growth occurs at the apex of each tip of the thallus. Translucent rhizoids, rootlike structures that are not absorptive, but primarily for anchoring the organism, sprout from the bottom of the plant.
Stoneworts have multicellular male and female sex organs (male = antheridium; female = oogonium), which grow at the nodes.
The name of these plants comes from the crust of white calcium carbonate seen in some species, which gives them a crunchy feel. Some species have a strong, musky smell, and are sometimes given the nickname "skunkweed" or "musk grass".
Chara is a species of particular interest in southern Florida, as it is a problematic invasive exotic that chokes canals and waterways throughout our area.

Only charophycean and land plant peroxisomes also contain enzymes that reduce the loss of the organic products via that old evolutionary relic, photorespiration.

Why would a terrestrial existence be an advantage for a plant? Why didn't they just stay in the water?
Items above that appear in [brackets] are found in all plants, but may also appear in a few highly derived green algae and/or charophytes.
In Bryophytes, the haploid gametophyte phase is the dominant life cycle phase, living more than one season.
The diploid sporophyte generation is small and ephemeral.

Liverwort gametophytes:
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Mosses and Hornworts have very similar life cycles, though the plants look somewhat different.
In all Bryophytes, the gametophyte is the long-living stage, whereas the sporophyte is ephemeral.
The situation is completely reversed in the...
The life cycle is similar in all tracheophytes, though--of course--the life cycle stages and the plants themselves look different. But the sporophytes, gametophytes and all associated structures of all the plants are homologous, no matter how different they might appear.
Cycads produce male and female cones on separate plants, and are thus dioecious.

The Anthophytes were traditionally divided into two main groups, the "dicots" and the "monocots"--so named because of the number of embryonic leaves (cotyledons) found in the embryos of each type of plant.
It's since become clear that these groupings do not reflect true evolutionary relationships: "monocots" are a highly derived, monophyletic group of plants that share a common ancestor with some of the "dicots." But what was once called "Dicotyledonae" is now recognized as a large assemblage of plants with sometimes distant evolutionary relationships.
Still, the physical characteristics of the two types of plants are useful because of the commercial importance of these plants, so here are some easy ways to tell the difference between them. (At least it will help you recognize the monophyletic monocots.)