Certainly! Below are the steps to configure and verify RIP (Routing Information Protocol) and EIGRP (Enhanced Interior Gateway Routing Protocol) routing protocols on a Cisco router:

### Configuring RIP (Routing Information Protocol):

1. **Enter Global Configuration Mode**:
   ```
   Router(config)# 
   ```

2. **Enable RIP on Interfaces**:
   ```
   Router(config)# router rip
   Router(config-router)# network <network_address>
   ```

3. **Optional: Set Passive Interfaces** (to prevent RIP updates on specific interfaces):
   ```
   Router(config-router)# passive-interface <interface>
   ```

4. **Verify RIP Configuration**:
   ```
   Router# show ip protocols
   Router# show ip route
   Router# show ip rip database
   Router# show ip rip neighbors
   Router# show ip rip interface
   ```

### Configuring EIGRP (Enhanced Interior Gateway Routing Protocol):

1. **Enter Global Configuration Mode**:
   ```
   Router(config)# 
   ```

2. **Enable EIGRP on Interfaces**:
   ```
   Router(config)# router eigrp <AS_number>
   Router(config-router)# network <network_address>
   ```

3. **Optional: Configure Route Summarization** (to reduce routing table size):
   ```
   Router(config-router)# eigrp <AS_number> summary-address <summary_address> <subnet_mask>
   ```

4. **Optional: Adjust Metric Weights** (to influence route selection):
   ```
   Router(config-router)# metric weights <K1> <K2> <K3> <K4> <K5>
   ```

5. **Verify EIGRP Configuration**:
   ```
   Router# show ip protocols
   Router# show ip route
   Router# show ip eigrp neighbors
   Router# show ip eigrp topology
   Router# show ip eigrp interface
   ```

### Verification:

After configuring either RIP or EIGRP, you can verify the routing protocol's operation and check for proper route propagation using the following commands:

- **Show IP Route**: Displays the router's routing table, showing all known routes.
- **Show IP Protocols**: Provides information about the configured routing protocols, including their status and parameters.
- **Show IP RIP Database** (for RIP) or **Show IP EIGRP Topology** (for EIGRP): Displays detailed information about learned routes and their metrics.
- **Show IP RIP/EIGRP Neighbors**: Shows neighboring routers participating in the routing protocol.
- **Show IP RIP/EIGRP Interface**: Provides details about interfaces enabled for RIP or EIGRP.

By using these commands, you can confirm that RIP or EIGRP has been correctly configured, check for neighbor adjacencies, verify learned routes, and ensure proper routing table population.

Remember to save your configurations using `write memory` or `copy running-config startup-config` to ensure that changes persist across router reboots. Additionally, always test network connectivity and monitor routing updates to ensure that the routing protocols are functioning as expected in your network environment.