Denormalizing With A Special Need

I have the following:

Demograph Table (PK MemberID)
-MemberID
-FirstName
-LastName

InsuranceSegments Table (PK = all columns combined)
-MemberID
-ProgramCode
-StatusCode
-BeginDate
-EndDate


I need to get the data into this table (i'll call the table MyTest)
-MemberID
-FirstName
-LastName
-BeginDate
-EndDate
-ProgramCode
-StatusCode

The catch:
For each record in the demograph table I need only one segment and that segment is to be based on the greatest EndDate.

What I need:
Give me the last segment for each demograph record and put each into it table MyTest

In my pseodo thinking
INSERT INTO MyTest (MemberID, FirstName, LastName, BeginDate, EndDate, ProgramCode, StatusCode)
SELECT
Demograph.MemberID, Demograph.FirstName, Demograph.LastName,
InsuranceSegments.BeginDate, InsuranceSegments.EndDate, InsuranceSegments.ProgramCode, InsuranceSegments.StatusCode
FROM
Demograph
INNER JOIN
InsuranceSegments
ON
Demograph.MemberID = InsuranceSegments.MemberID
WHERE { Need help :-) }
Need help with the where clause to get the segment with the 'highest/latest' EndDate


Sorry for the wall of text. I hope this is enough information to receive help and would like to thank you in advance for your time :-)

J