Question

How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a 4 x 4 square array of dots?

Answer 1

The answer is:  9

There are 9 kinds of non-congruent isosceles triangles that can be formed by connecting three of the dots in a 4 x 4 square array of dots

The attached figure represents the explanation of the answer.

Answer 2

By connecting three of the dots in a $4\times 4$ square array of dots,  $\boxed{\bf 9}$ different non-congruent isosceles triangles can be formed.

Further explanation:

An isosceles triangle is a triangle whose two sides are equal. The length of the two sides is equal and the angles opposite to equal sides are also equal.

The two isosceles triangles are congruent to each other if the triangles are copy of each other.

By connecting three dots in a $4\times 4$ square array of dots many triangles can be formed.

In a $4\times 4$ square array of dots, $9$ different isosceles triangles are formed by connecting three dots.

In the Figure 1 it is observed that a triangle $\triangle{\text{ ABC}}$  is formed in a $4\times 4$ square array therefore, the length AB is equal to the length BC.

Thus, the $\triangle\text{ ABC}$ is an isosceles triangle.

Similarly, the triangles $\triangle\text{A'B'C'}$,$\triangle\text{DEO}$,$\triangle\text{D'E'O'}$,$\triangle\text{GHI}$,$\triangle\text{G'H'I'}$,$\triangle\text{JKL}$,$\triangle\text{J'K'L'}$,$\triangle\text{XYZ}$ are the isosceles triangles.

From attached Figure 1 and Figure 2 it can be seen that sides of the $\triangle\text{ ABC}$ are not same as the sides of the triangle $\triangle\text{ A'B'C'}$.

Therefore, the triangles $\triangle\text{ ABC}$ and $\triangle\text{ A'B'C'}$ are non-congruent triangle.

It is observed from Figure 1 and Figure 3 that the sides of the triangle $\triangle\text{ ABC}$ are not same as the sides of the triangle $\triangle\text{ DEO}$.

Therefore, the triangles $\triangle\text{ ABC}$ and $\triangle\text{ DEO}$ are non-congruent triangle.

Similarly, all the $\boxed{\bf 9}$ triangles formed are non-congruent to each other.

Learn more:

1. Learn more about problem on numbers: brainly.com/question/1852063

2. Learn more about problem on function brainly.com/question/3225044

3. Learn more about problem on triangle brainly.com/question/7437053

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Triangles

Keywords: Triangle, isosceles triangle, dots, square, 4*4, congruent, length, sides, corresponding angles, array, congruency, non-congruency.