"head" sounds:

• head

• shepherd

• leg

• met 

"hate" sounds:

• hate

• shape

• lake

• mate 

We make the sound in "head" with our mouth open wider than for /i/ or /I/ and our tongues not as close to the top of our mouths.

The sound in "hate" is actually a dipthong, which means it is a combination of the sounds /e/ and /I/. You can feel your tongue moving closer to the roof of your mouth when you say it.