Write a program to prompt user for an integer and display a triangle of stars with the same height as the input provided by the user. For example:

Here is a simple Python program that accomplishes this task:

# Prompt the user for an integer
height = int(input("Enter the height of the triangle: "))

# Loop through each row of the triangle
for i in range(height):
    # Calculate the number of spaces and stars for this row
    spaces = ' ' * (height - i - 1)
    stars = '*' * (2 * i + 1)
    
    # Print the row
    print(spaces + stars)

This program works by looping through each row of the triangle. For each row, it calculates the number of spaces and stars needed, and then prints them. The number of spaces is equal to the height of the triangle minus the current row number (starting from 0), and the number of stars is equal to twice the current row number plus one. This ensures that the triangle is centered and has the correct number of stars on each row.