Question

which triangle(s) would help us to use the pythagorean theorem and solve for the distance between points l and m?
○ triangle a
○ triangles b and c
○ triangles a and d
○ triangle c

Explanation:

To use the Pythagorean theorem for the distance between \( L \) and \( M \), the triangle formed should be a right - triangle with legs parallel to the axes (so that the lengths of the legs can be easily determined from the grid). Triangles A and D are right - triangles where the horizontal and vertical distances between the points (which form the legs of the right - triangle) can be used in the Pythagorean theorem (\( c=\sqrt{a^{2}+b^{2}} \), where \( c \) is the distance between \( L \) and \( M \), and \( a,b \) are the horizontal and vertical leg lengths) to find the distance between \( L \) and \( M \). Other triangles either do not form a right - triangle suitable for this or have legs that are not aligned in a way that allows easy calculation of the horizontal and vertical differences.

Answer:

Triangles A and D