Question

Name each part of octagon MNOPQRST. two consecutive vertices

Short answer

One example of two consecutive vertices is M and N.

Step-by-step solution

Understand the Problem

The problem asks us to identify two consecutive vertices of the octagon MNOPQRST. An octagon is a polygon with eight sides and vertices. In this case, the vertices are labeled as M, N, O, P, Q, R, S, and T.

Identify Consecutive Vertices

Consecutive vertices in a polygon are vertices that are connected directly by a side or edge. To find two consecutive vertices, look at the sequence of vertex labels and identify any two that are next to each other without any skips.

Choose Two Consecutive Vertices

From the list of vertices MNOPQRST, two consecutive vertices can be chosen. For example, M and N are consecutive, as are N and O, O and P, and so on. An alternative pair can be P and Q, Q and R, R and S or S and T.

Select for the Answer

Select one pair of consecutive vertices as the answer. Picking any one of these pairs—say M and N—will address the problem requirement.

Key concepts

Vertices

In any geometric shape, such as a polygon, vertices are crucial components. Vertices are points where two or more lines meet to form an angle. In an octagon, which is an eight-sided polygon, there are exactly eight vertices. These vertices are typically labeled with letters for ease of reference.

In the case of an octagon labeled MNOPQRST, each letter represents a single vertex.

• M is one vertex.
• N is another vertex.
• And so on up to T.

Understanding what a vertex is can help you visualize the structure of the octagon. Recognizing each vertex allows you to better grasp how the octagon is formed and to solve related problems effectively.

Polygon

A polygon is a two-dimensional shape that has straight sides. These sides come together to form vertices. One common example is an octagon, which has eight sides and vertices. Polygons are classified based on the number of sides they have:

• A triangle has three sides.
• A quadrilateral has four sides.
• An octagon, like MNOPQRST, has eight sides.

Polygons are closed shapes, meaning all their lines connect with no gaps.

Polygons can be regular or irregular. In a regular polygon, all sides and angles are equal. An octagon can be regular with equal sides, or it can be irregular if the sides vary in length.

Consecutive Vertices

In the context of polygons, understanding consecutive vertices is simple but essential. Consecutive vertices are pairs of vertices connected by a single line segment or edge of the polygon. They are "next to" each other in a sequence, like letters on a string.

Take the octagon MNOPQRST, where each letter represents a vertex. To find consecutive vertices, you look for adjacent pairs without any skips:

• M and N are consecutive because there is a side between them.
• N and O follow the same rule.
• This applies all the way from M and N to S and T.

Recognizing consecutive vertices is important for solving many geometrical problems, as they often determine the shape and path within the polygon.