Constructions
Table of Contents
- Tools (introduction)
- Line Segments
- Copying a Line Segment
- Bisecting a Line Segment
- Angles
- Copying an Angle
- Bisecting an Angle
- Lines
- Perpendicular to a Line Through a Point on the Line
- Perpendicular to a Line Through a Point Not on the Line
- Parallel Line Through a Point - Perpendicular Lines
- Parallel Line Through a Point - Angle Copy
- Triangles
- Extra
- Construction Template
Copying a Line Segment
Given a line segment [math]AB[/math],[br][br][list][*] Create point [math]C[/math] not on [math]\overline{AB}[/math][br][br][/*][*] Using the [b]Compass tool[/b], create a circle with radius [math]m\overline{AB}[/math] centered @ point [math]C[/math][br][br][/*][*] Using the [b]Point on Object tool[/b], create a point on the circle ([math]D[/math])[br][br][/*][*] Using the [b]Segment tool[/b], create [math]\overline{CD}[/math][br][/*][/list]
What is the relationship between [math]\overline{AB}[/math] and [math]\overline{CD}[/math]? [i]HINT[/i]: Use the [b]Distance or Length tool[/b][br][br][br]Does your construction pass the Drag Test?
Copying an Angle
Given some angle [math]ABC[/math],[br][list][br][*] Create points [math]D[/math] and [math]E[/math] not on [math]\overline{BA}[/math] or [math]\overline{BC}[/math][br][br][/*][*] Using the [b]Segment tool[/b], construct line segment [math]\overline{DE}[/math][br][br][/*][*] Create point [math]F[/math] on [math]\overline{BA}[/math][br][br][/*][*] Using the [b]Compass tool[/b], create circle [math]d[/math] with radius [math]m\overline{BF}[/math] centered @ [math]B[/math][br][br][/*][*] Using the [b]Intersect tool[/b], create the point of intersection [math]G[/math] between [math]\overline{BC}[/math] and circle [math]d[/math][br][br][/*][*] Using the [b]Compass tool[/b], create circle [math]e[/math] with radius [math]m\overline{BF}[/math] centered @ [math]D[/math][br][br][/*][*] Using the [b]Intersect tool[/b], create the point of intersection [math]H[/math] between circle [math]e[/math] and [math]\overline{DE}[/math][br][br][/*][*] Using the [b]Compass tool[/b], create circle [math]f[/math] with radius [math]m\overline{FG}[/math] centered @ [math]H[/math][br][br][/*][*] Using the [b]Intersect tool[/b], create the points of intersection [math]I[/math] and [math]J[/math] between circles [math]e[/math] and [math]f[/math][br][br][/*][*] Using the [b]Ray tool[/b], construct [math]\overrightarrow{DI}[/math][br][/*][/list]
What relationship exists between [math]\angle{ABC}[/math] and [math]\angle{EDI}[/math]? [i]HINT[/i]: use the [b]Angle tool[/b][br][br][br]Does your construction pass the Drag Test?
Perpendicular to a Line Through a Point on the Line
Given a point [math]C[/math] on some line [math]AB[/math],[br][list][br][*] Create point [math]D[/math] on [math]\overleftrightarrow{AB}[/math] such that [math]{D}\neq{C}[/math][br][br][/*][*] Using the [b]Compass tool[/b], create a circle [math]c[/math] with radius [math]m\overline{DC}[/math] centered @ point [math]C[/math][br][br][/*][*] Using the [b]Point tool[/b], create the OTHER point of intersection ([math]E[/math]) between circle [math]c[/math] and [math]\overleftrightarrow{AB}[/math][br][br][/*][*] Using the [b]Compass tool[/b], create a circle [math]d[/math] with radius [math]m\overline{DE}[/math] centered @ point [math]D[/math][br][br][/*][*] Using the [b]Compass tool[/b], create a circle [math]e[/math] with radius [math]m\overline{DE}[/math] centered @ point [math]E[/math][br][br][/*][*] Using the [b]Intersect tool[/b], create the points of intersection [math]F[/math] and [math]G[/math] between circles [math]d[/math] and [math]e[/math][br][br][/*][*] Using the [b]Line tool[/b], create [math]\overleftrightarrow{FG}[/math][br][/*][/list]
Does your construction pass the Drag Test?