SharedSizeGroup on dataGrid

I have a DataGrid and a grid on my WPF application and I want their respected columns be the same size. I thought maybe I use SharedSizeGroup but it seems that DataGrid columns don’t have this property (Am I wrong?). How can I do this?

Update1

I changed the xaml as follow:

<Grid>
    <Grid.RowDefinitions>
        <RowDefinition Height="20" MaxHeight="开发者_如何学Go20" MinHeight="20" />
        <RowDefinition />
    </Grid.RowDefinitions>
    <Grid >
        <Grid.ColumnDefinitions >
            <ColumnDefinition   Width="{Binding ElementName=titleDataGridColumn, Path=ActualWidth}" />
            <ColumnDefinition   Width="{Binding ElementName=forenameDataGridColumn, Path=ActualWidth}"/>
            <ColumnDefinition   Width="{Binding ElementName=surnameDataGridColumn, Path=ActualWidth}" />
            <ColumnDefinition   Width="{Binding ElementName=dobDataGridColumn, Path=ActualWidth}" />
            </Grid.ColumnDefinitions>
        <Button Content="Clear" HorizontalAlignment="Stretch" Name="searchClearButton" VerticalAlignment="Stretch"   Grid.Column="0" Click="searchClearButton_Click" />
        <TextBox HorizontalAlignment="Stretch"  Name="forenameTextBox" VerticalAlignment="Stretch" Grid.Column="1" />
        <TextBox HorizontalAlignment="Stretch"  Name="surnameTextBox" VerticalAlignment="Stretch" Grid.Column="2" />
        <TextBox HorizontalAlignment="Stretch"  Name="dobTextBox" VerticalAlignment="Stretch" Grid.Column="3" />

    </Grid>

    <DataGrid Grid.Row="1" x:Name="DataDataGrid" HorizontalAlignment="Stretch" AutoGenerateColumns="False" VerticalAlignment="Stretch"  ItemsSource="{Binding}" AlternationCount="1"  IsReadOnly="True" SelectionMode="Single" >
        <DataGrid.Columns>
            <DataGridTextColumn x:Name="titleDataGridColumn" Binding="{Binding Path='Title'}" Header="Title" Width="35*"    />
            <DataGridTextColumn x:Name="forenameDataGridColumn" Binding="{Binding Path='Forename'}" Header="Forename" Width="65*" />
            <DataGridTextColumn x:Name="surenameDataGridColumn" Binding="{Binding Path='Surname'}" Header="Surname" Width="65*"/>
            <DataGridTextColumn x:Name="dobDataGridColumn" Binding="{Binding DOB,StringFormat={}\{0:dd/MM/yyyy\}}"  Header="DOB" Width="70*"/>
        </DataGrid.Columns>
    </DataGrid>

</Grid>

But now the surname column in grid is bigger than its corresponding column in datagrid and the button is a bit to left ( could be fixed by setting margin on grid column) but I cannot understand why surname columns are not same size?

Update 2

This is working (Problem was the surenameDataGridColumn was not correct (spelling))

<Grid>
    <Grid.RowDefinitions>
        <RowDefinition Height="20" MaxHeight="20" MinHeight="20" />
        <RowDefinition />
    </Grid.RowDefinitions>
    <Grid >
        <Grid.ColumnDefinitions >
            <ColumnDefinition Width="6px"/>
            <ColumnDefinition   Width="{Binding ElementName=titleDataGridColumn, Path=ActualWidth}" />
            <ColumnDefinition   Width="{Binding ElementName=forenameDataGridColumn, Path=ActualWidth}"/>
            <ColumnDefinition   Width="{Binding ElementName=surnameDataGridColumn, Path=ActualWidth}" />
            <ColumnDefinition   Width="{Binding ElementName=dobDataGridColumn, Path=ActualWidth}" />
        </Grid.ColumnDefinitions>
        <Button Content="Clear" HorizontalAlignment="Stretch" Name="searchClearButton" VerticalAlignment="Stretch"   Grid.Column="1" Click="searchClearButton_Click" />
        <TextBox HorizontalAlignment="Stretch"  Name="forenameTextBox" VerticalAlignment="Stretch" Grid.Column="2" />
        <TextBox HorizontalAlignment="Stretch"  Name="surnameTextBox" VerticalAlignment="Stretch" Grid.Column="3" />
        <TextBox HorizontalAlignment="Stretch"  Name="dobTextBox" VerticalAlignment="Stretch" Grid.Column="4" />
       </Grid>

    <DataGrid Grid.Row="1" x:Name="DataGrid" HorizontalAlignment="Stretch" AutoGenerateColumns="False" VerticalAlignment="Stretch"  ItemsSource="{Binding}" AlternationCount="1"  IsReadOnly="True" >
        <DataGrid.Columns>
            <DataGridTextColumn x:Name="titleDataGridColumn" Binding="{Binding Path='Title'}" Header="Title" Width="35*"    />
            <DataGridTextColumn x:Name="forenameDataGridColumn" Binding="{Binding Path='Forename'}" Header="Forename" Width="65*" />
            <DataGridTextColumn x:Name="surnameDataGridColumn" Binding="{Binding Path='Surname'}" Header="Surname" Width="65*"/>
            <DataGridTextColumn x:Name="dobDataGridColumn" Binding="{Binding DOB,StringFormat={}\{0:dd/MM/yyyy\}}"  Header="DOB" Width="70*"/>
       </DataGrid.Columns>
    </DataGrid>
</Grid>

By adding a new column, I aligned the left of button with the left of Title column in DataGrid.

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Use binding to bind the Grid column widths to the size of the columns in your DataGrid. For example:

<dg:DataGridTextColumn x:Name="FirstColumn" Header="Text"/>

<ColumnDefinition Width="{Binding ElementName=FirstColumn, Path=ActualWidth}"/>