The branches Radiata and Bilateria of the Eumetazoa both exhibit :

Options

A. cephalization
B. dominance of diploid life stage
C. a complete digestive tract with separate mouth and anus
D. three germ layers in embryonic development

Explanation

To solve the question regarding the branches Radiata and Bilateria of the Eumetazoa, we will analyze the options provided and determine which characteristic is shared by both branches.

### Step-by-Step Solution:

1. **Understanding Eumetazoa**:
- Eumetazoa is a clade that includes all animals except for sponges (Phylum Porifera). It is divided into two main branches: Radiata and Bilateria.

2. **Analyzing the Options**:
- **Option A: Cephalization**: This refers to the concentration of sensory organs and nervous tissue at the anterior end of the organism, forming a head. Radiata (like cnidarians) do not exhibit true cephalization, while Bilateria do. Therefore, this option is incorrect for both.

- **Option B: Dominance of diploid life stage**: Most multicellular organisms, including those in Radiata and Bilateria, have a life cycle dominated by the diploid stage, where the haploid stage is reduced. This option is likely correct.

- **Option C: A complete digestive tract with separate mouth and anus**: This characteristic is found in more complex organisms, particularly in Bilateria. Radiata typically do not have a complete digestive tract, as they have a gastrovascular cavity. Thus, this option is incorrect.

- **Option D: Three germ layers in embryonic development**: Radiata organisms (like cnidarians) are diploblastic, meaning they have two germ layers (ectoderm and endoderm), while Bilateria are triploblastic (having three germ layers: ectoderm, mesoderm, and endoderm). Therefore, this option is also incorrect.

3. **Conclusion**:
- After analyzing all the options, the correct answer is **dominance of diploid life stage** since both Radiata and Bilateria exhibit this characteristic.

### Final Answer:
The branches Radiata and Bilateria of the Eumetazoa both exhibit **dominance of diploid life stage**.

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