Geometry: Compass and Straightedge Constructions

Geometric Construction

Compass and Straightedge

• A compass is a tool used to draw circles and arcs
• A straightedge (or ruler) is a tool used to draw straight lines
• These two tools are the only ones allowed in traditional geometric constructions
• They are used to create geometric shapes and figures according to specific rules

Classic Constructions

• Equilateral Triangle
  • Construction: Place the point of the compass on one end of a line segment, open the compass to the length of the segment, and draw an arc above the segment
  • Repeat the process on the other end of the segment, and where the two arcs intersect is the third vertex of the equilateral triangle
• Perpendicular Line
  • Construction: Place the point of the compass on a point on a line, open the compass to a convenient radius, and draw an arc above and below the line
  • Draw a line through the point and the point where the two arcs intersect
• Angle Bisector
  • Construction: Place the point of the compass on the vertex of an angle, open the compass to a convenient radius, and draw an arc above and below the angle
  • Draw a line through the vertex and the point where the two arcs intersect
• Regular Polygon
  • Construction: Use the compass to draw a circle and then use the straightedge to draw radii that divide the circle into equal parts
  • The points where the radii intersect the circle are the vertices of the regular polygon

Geometric Construction Tools

• A compass is used to draw circles and arcs
• A straightedge (or ruler) is used to draw straight lines
• These two tools are the only ones allowed in traditional geometric constructions

Classic Geometric Constructions

Equilateral Triangle

• Constructed by placing the compass point on one end of a line segment and drawing an arc above the segment
• Repeating the process on the other end of the segment, and where the two arcs intersect is the third vertex of the equilateral triangle

Perpendicular Line

• Constructed by placing the compass point on a point on a line, opening the compass to a convenient radius, and drawing an arc above and below the line
• Drawing a line through the point and the point where the two arcs intersect

Angle Bisector

• Constructed by placing the compass point on the vertex of an angle, opening the compass to a convenient radius, and drawing an arc above and below the angle
• Drawing a line through the vertex and the point where the two arcs intersect

Regular Polygon

• Constructed by using the compass to draw a circle and then using the straightedge to draw radii that divide the circle into equal parts
• The points where the radii intersect the circle are the vertices of the regular polygon

Text Editing

• Basic editing operations include insertion, deletion, and replacement of text at the cursor position
• Text manipulation features include cut, copy, and paste functions, as well as undo and redo capabilities

Text Selection

• Text can be selected using the mouse or keyboard
• Selecting all text can be done using the Ctrl+A shortcut

Find and Replace

• The find function allows searching for specific text patterns
• The replace function allows replacing found text with new text

Font Management

Font Types

• Serif fonts (e.g. Times New Roman) have serifs (small lines) at the ends of strokes
• Sans-serif fonts (e.g. Arial) do not have serifs
• Monospace fonts (e.g. Courier) have fixed-width characters

Font Styles

• Bold style makes text thicker and heavier
• Italic style slants text to the right
• Underline style adds a horizontal line below text
• Strikethrough style adds a horizontal line through text

Font Sizes and Colors

• Point sizes (e.g. 12pt) specify font size in points
• Relative sizes (e.g. larger, smaller) specify font size relative to the surrounding text
• Text color specifies the color of the text
• Background color specifies the color behind the text

Table Creation

Table Structure

• Tables consist of rows and columns, which intersect to form cells

Table Formatting

• Border styles include solid, dashed, and others
• Border widths specify the thickness of table borders
• Cell padding and spacing specify the distance between cell contents and borders

Table Operations

• Rows and columns can be inserted or deleted
• Cells can be merged or split
• Columns and rows can be resized

Document Formatting

Page Layout

• Margins specify the distance between the text and the page edges
• Orientation specifies whether the page is portrait (vertical) or landscape (horizontal)
• Paper size specifies the size of the paper

Section Formatting

• Headers and footers specify text that appears at the top or bottom of each page
• Page breaks specify where one page ends and another begins
• Section breaks specify where one section ends and another begins

Paragraph Formatting

• Alignment specifies how text is positioned horizontally (left, center, right, justified)
• Indentation specifies how much text is indented from the left margin
• Line spacing specifies the distance between lines of text