Which of the following will not show cis-trans isomerism?

Options

A. Butanedioic acid
B. `1,2`-dimethyl cyclopropane
C. `1,2`-dichloroethene
D. Butanedioic acid

Explanation

To determine which of the given compounds will not show cis-trans isomerism, we need to analyze the structures of each compound based on the criteria for cis-trans isomerism.

### Step-by-Step Solution:

1. **Understanding Cis-Trans Isomerism**:
- Cis-trans isomerism occurs in compounds that have restricted rotation around a double bond or within a ring structure. For cis isomers, similar groups are on the same side, while for trans isomers, they are on opposite sides.

2. **Analyzing Each Compound**:
- **Compound A: Butane-1,2-dioic acid (HOOC-CH2-CH2-COOH)**:
- This compound does not have any double bonds or rings. It is a straight-chain dicarboxylic acid. Therefore, it cannot exhibit cis-trans isomerism.

- **Compound B: 1,2-Dimethylcyclopropane**:
- This compound has a cyclopropane ring with two methyl groups attached to adjacent carbons. The presence of the ring structure allows for cis-trans isomerism, as the two methyl groups can be on the same side (cis) or opposite sides (trans) of the ring.

- **Compound C: 1,2-Dichloroethene (C2H2Cl2)**:
- This compound has a double bond between two carbon atoms, with chlorine atoms attached to each carbon. The double bond restricts rotation, allowing for cis (both Cl on the same side) and trans (Cl on opposite sides) isomers.

- **Compound D: Butene-1,2-dioic acid (HOOC-CH=CH-COOH)**:
- This compound contains a double bond between two carbon atoms, which allows for cis-trans isomerism. The carboxylic acid groups can be positioned in different orientations relative to the double bond.

3. **Conclusion**:
- Among the given compounds, **Butane-1,2-dioic acid (Compound A)** is the only one that does not show cis-trans isomerism due to the absence of a double bond or ring structure.

### Final Answer:
**Butane-1,2-dioic acid (Compound A) will not show cis-trans isomerism.**