Objects > Angle Markers and Tick Marks

Use angle markers to draw attention to an angle, to measure an angle, or to denote special relationships such as congruent angles. Angle markers are normally displayed as filled arcs. When you drag or construct an angle so that it's a right angle, the marker is displayed as a right-angle marker.

You cannot trace, transform, or iterate angle markers.

Note

Sketchpad doesn't detect congruent angles automatically, but leaves it up to you to form and test conjectures by making appropriate observations and measurements. You can use angle markers to indicate confirmed conjectures, untested conjectures, or in any other way that you find useful.

There are two ways to create an angle marker:

•Drag the Marker tool from one side of the angle to the other.

•Drag the Marker tool from the vertex to the interior of the angle.

If there are several possible angles with the same vertex, the position to which you drag determines which angle is marked.

Note

While you are editing a caption, use either method to create a new angle marker and insert a Hot Text link into the caption.

Angle markers can be defined in four ways.

Definition	Example	Magnitude(degrees)	Magnitude (directed degrees)	Magnitude (radians)
Simple: A simple angle is always less than or equal to a straight angle. It represents the smallest turn at the vertex from the initial ray (or first point) to the terminal ray (or third point). Its direction can be counter-clockwise or clockwise.		0° ≤ θ ≤ 180°	–180° < θ ≤ 180°	–π < θ ≤ π
Reflex: A reflex angle is always greater than or equal to a straight angle. It represents the greatest turn at the vertex from the initial ray (or first point) to the terminal ray (or third point). Its direction can be counter-clockwise or clockwise.		180° ≤ θ ≤ 360°	180° ≤ θ ≤ 360° or –360° < θ < –180°	π ≤ θ ≤ 2π or –2π < θ < –π
Counter-clockwise: A counter-clockwise angle represents the counter-clockwise turn at the vertex from the initial ray (or first point) to the terminal ray (or third point). It can be either simple or reflex.		0° ≤ θ < 360°	0° ≤ θ < 360°	0 ≤ θ < 2π
Clockwise: A clockwise angle represents the clockwise turn at the vertex from the initial ray (or first point) to the terminal ray (or third point). It can be either simple or reflex.		0° ≤ θ < 360°	–360° < θ ≤ 0°	–2π < θ ≤ 0

When you use the Marker tool to create an angle marker, the resulting angle marker is either simple or reflex depending on the direction in which you drag.

To change an angle marker to use a different definition, select it and choose Edit | Properties | Marker.

If a simple, counter-clockwise, or clockwise angle marker has a magnitude of exactly 90°, it appears as a right-angle marker.

Angle markers display one or more closely spaced strokes, the region defined by the innermost stroke, and an optional arrowhead to indicate direction.

When the marked angle is a right angle, the stroke(s) form a customary right-angle marker. Otherwise the strokes appear as arcs.

•To change the number of strokes, click the angle marker with the Marker tool.

•To set the color of the marker, choose Display | Color.

•To set the thickness of the marker’s stroke(s), choose Display | Line Style.

•To set the radius of the stroke(s), choose Display | Point Style.

•To change the definition of the marker, the number of strokes, and whether or not an arrowhead appears, choose Edit | Properties | Marker.

•To determine the transparency of the region, choose Edit | Properties | Opacity. You can make the region completely transparent, so that only the stroke(s) are visible.

To measure an angle, select an angle marker and choose Measure | Angle.

To use an angle marker as a marked angle for rotation or polar translation, select it and choose Transform | Mark Angle, or click the angle marker in the sketch while using the Rotation or Translation dialog box.

To create an angle marker while you’re editing a caption, press and drag in the sketch to designate the angle, just as you would using the Marker tool. Sketchpad creates the angle marker and inserts a Hot Text link into the caption in one step.