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
. Early Cousins of Land Plants: Zygnematales The Zygnematales are (haploid) green algae that undergo sexual reproduction via conjugation: haploid vegetative cells in the algal adult form non-flagellated gametes. Complementary (+ and - types) gametes fuse to form a zygote. There are many variations on the conjugation theme, but one example is nicely shown in Spirogyra:

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.
Early Cousins of Land Plants: Charales The Charales, aslo known as stoneworts or brittleworts, are common in slow-moving, often eutrophic freshwater habitats, and are found on every continent except Antarctica.
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.

Early Cousins of Land Plants: Coleochaetales There are fifteen extant species of Coleochaete, of interest to systematists because they appear to be the closest living relatives of land plants. What characters do they share?
Only charophycean and land plant peroxisomes also contain enzymes that reduce the loss of the organic products via that old evolutionary relic, photorespiration.

Land Plants: Evolutionary History and Diversity Land plants all produce embryos that develop inside the tissues of a maternal plant. This is where the taxon gets its name. All embryophytes are primitively land-dwelling, though some are not entirely free of a need for water in the environment, especially for reproduction.
Why would a terrestrial existence be an advantage for a plant? Why didn't they just stay in the water?
Embryophyta: The Land Plants
What makes land plants different from other members of Viridaeplantae?
Several synapomorphies link all land plants together and distinguish them
from their algal relatives:
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.
Embryophyta: An Overview
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.
An Overview of Plant Taxa
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.)