Question

The points of this 3-by-3 grid are equally spaced horizontally and vertically. How many non-congruent isosceles triangles can be formed using three points of this grid?

a. 6
b. 9
c. 12
d. 18

Answer 1

There are 12 non-congruent isosceles triangles that can be formed using three points from the 3x3 grid.

Step-by-step explanation:

An isosceles triangle has two sides that are equal in length. In a 3x3 grid, there are multiple ways to form isosceles triangles using three points.

To determine the number of non-congruent isosceles triangles, we need to consider the different cases:

1. Triangles with one horizontal side and two diagonal sides: There are two ways to choose the horizontal side and two ways to choose the diagonal sides. So, there are 2 x 2 = 4 triangles.
2. Triangles with one vertical side and two diagonal sides: Similar to the first case, there are 4 triangles.
3. Triangles with two vertical sides and one horizontal side or two horizontal sides and one vertical side: There are 4 right triangles that fit into this category.

In total, there are 4 + 4 + 4 = 12 non-congruent isosceles triangles that can be formed using three points from the 3x3 grid.