louis drew all of the possible diagonals from one vertex of a regular hexagon. Which of these statements is true?
A) Each diagonal from this vertex is one of two different lengths
B) None of the diagonals forms a line of symmetry of the hexagon.
C) The diagonals form four congruent triangles.
D) All of the diagonals from this vertex are congruent.
The correct statement is D) All of the diagonals from this vertex are congruent.
To determine which statement is true, let's analyze each option:
A) Each diagonal from this vertex is one of two different lengths:
To verify this statement, we need to understand how many diagonals can be drawn from a single vertex of a regular hexagon.
A regular hexagon has six vertices. If we choose one vertex, we can draw diagonals to the remaining five vertices, creating a total of five diagonals.
Now, if we carefully observe the hexagon, we can see that all the sides of the hexagon are congruent, which means they have the same length. Therefore, each diagonal from one vertex will have a different length. So, statement A is not true.
B) None of the diagonals forms a line of symmetry of the hexagon:
To investigate this statement, we need to examine if any of the diagonals match the hexagon's lines of symmetry.
A line of symmetry divides a figure into two identical halves. In a regular hexagon, there are three lines of symmetry, passing through opposite vertices, and each line of symmetry divides the hexagon into two congruent halves.
However, if we draw the diagonals from one vertex, we can observe that none of the diagonals align with the lines of symmetry. Therefore, statement B is true.
C) The diagonals form four congruent triangles:
To evaluate this statement, we will examine if the diagonals create congruent triangles.
By drawing all the diagonals from one vertex, we can see that they divide the hexagon into four triangles. However, these triangles are not necessarily congruent. The diagonals may have different lengths, resulting in triangles with different side lengths. Therefore, statement C is not true.
D) All of the diagonals from this vertex are congruent:
To confirm this statement, we need to check if all the diagonals from one vertex have the same length.
Looking at the regular hexagon, we can see that all the sides have the same length. If we draw the diagonals from one vertex, we'll notice that they are equal in length. Therefore, statement D is true.
In conclusion, the correct statement is D) All of the diagonals from this vertex are congruent.