Question

prepare for transformations in the coordinate plane
1 think about what you know about geometric figures and vertices. fill in each box.
use words, numbers, and pictures. show as many ideas as you can.
(concept map: vertex at center, connected to what is it?, what i know about it, examples, non-examples boxes)
2 how many vertices does each figure have?
(images: rectangle, octagon, circle)

Explanation:

Part 1: Filling the "vertex" concept map

What Is It?

A vertex (plural: vertices) is a point where two or more line segments or edges meet in a geometric figure (like a corner of a polygon or the intersection of edges in a 3D shape).

What I Know About It

• Vertices are defined by coordinates in a coordinate plane (e.g., \((x, y)\) in 2D, \((x, y, z)\) in 3D).
• The number of vertices relates to the type of polygon (e.g., triangle has 3, quadrilateral has 4).
• Vertices help define the shape and structure of geometric figures.

Examples

• Triangle: 3 vertices (e.g., \(A(0,0)\), \(B(2,0)\), \(C(1,2)\)).
• Square: 4 vertices (e.g., \(A(0,0)\), \(B(2,0)\), \(C(2,2)\), \(D(0,2)\)).
• Cube (3D): 8 vertices.

Non - Examples

• A line segment: has no vertices (it’s a straight path between two points, but the endpoints are not "corners" of a closed figure in the same sense; or, more clearly, a curved line or a circle— a circle has no vertices, as it has no straight edges meeting at a point).

Part 2: Number of vertices for each figure

Rectangle (First figure)

Step 1: Recall rectangle properties

A rectangle is a quadrilateral with 4 right angles and 4 sides. By definition, a quadrilateral has 4 vertices (the corners where the sides meet).

Regular Octagon (Second figure)

Step 1: Recall octagon properties

A regular octagon is a polygon with 8 equal - length sides. A polygon with \(n\) sides has \(n\) vertices. For an octagon, \(n = 8\), so it has 8 vertices.

Circle (Third figure)

Step 1: Recall circle properties

A circle is a curved shape with no straight edges. Since vertices are points where straight edges meet, a circle has no vertices (0 vertices).

Answer:

s:

Part 1 (Concept Map):

• What Is It?: A point where two or more line segments/edges meet in a geometric figure.
• What I Know About It: Defined by coordinates; number relates to polygon type; defines shape/structure.
• Examples: Triangle (3), Square (4), Cube (8) (with coordinates or descriptions).
• Non - Examples: Line segment (no vertices in the "corner" sense), Circle (no straight edges to meet at a point).

Part 2 (Number of Vertices):

• Rectangle: 4
• Regular Octagon: 8
• Circle: 0