<angle>

<angle> is a Graphical component which renders a geometric angle when nested inside a <graph> component.

Attributes and Properties

Example: Angle between two lines

<graph size="small" xmax="6" ymin="-6">
  <line name="line1">y = 1/2 x + 4</line>
  <line name="line2">y = -x  - 1</line>
  <angle betweenLines="$line1 $line2" radius="3"/>
</graph>

Two lines are created within a <graph> using the <line> component. The <angle> component is specified by referencing those lines by name with the betweenLines attribute.

Example: Angle between three points

<graph size="small" xmin="-6" xmax="6" ymin="-6" ymax="6">
  <angle through="(5,-3) (0,0) (5,4)"/>
</graph>

Three points define the angle with the through attribute.

Example: Angle specified by user-input

The user is prompted to enter an angle with the <mathInput/> component. This angle is then referenced by name within the opening and closing <angle> tags.

Attribute Example: radius

  <graph size="small">
    <angle degrees="65" radius="5"/>
  </graph>

The radius attribute is used to change the radius of the angle symbol shown on the graph. Default = 1; type = math.

Attribute Example: chooseReflexAngle

The chooseReflexAngle attribute is used to change the behavior of angle representation, where more than one angle is possible. The attribute accepts three possible text values: always, never (default), and allowed.

The blue angle in the graph illustrates the condition where the default condition where the reflex angle (or angle greater than $180^\circ$) is never selected.

By contrast, the red angle illustrates the condition where the reflex angle is always selected.

Finally, the orange angle takes the specified through-points in a counter-clockwise direction and illustrates the case where chooseReflexAngle = "allowed" has been selected. The resulting angle may be a reflex angle or not a reflex angle depending on the position of the points. Try dragging the red square (point C) to observe this difference in behavior. Default = “never”; type = text.

Attribute Example: inDegrees

<graph size="small" xmin="-3" xmax="3" ymin="-3" ymax="3">
  <angle name="a" inDegrees degrees="30"/>
</graph>
The angle <m>a</m> is $a

The inDegrees attribute specifies that the output of the angle when defined or copied outside the graph should have units of degrees. Default = “false”; type = boolean.

Attribute Example: degrees

<graph size="small" xmin="-3" xmax="3" ymin="-3" ymax="3">
  <angle degrees="30"/>
</graph>

The degrees attribute specifies the measure of the angle in degrees; type = math.

Attribute Example: radians

<graph size="small" xmin="-3" xmax="3" ymin="-3" ymax="3">
  <angle radians="pi/2"/>
</graph>

The radians attribute specifies the measure of the angle in radians; type = math. Note that radians are the default units for angles in DoenetML.

Attribute Example: through

The through attribute accepts three points through which to construct the angle. Type = pointList.

Attribute Example: betweenLines

The betweenLines attribute accepts two lines to construct the angle between. Type = lineList.

Attribute Example: emphasizeRightAngle

<graph size="small" xmin="-3" xmax="3" ymin="-3" ymax="3">
  <angle radians="pi/2" emphasizeRightAngle="false"/>
</graph>

By default, right angles are shown with a square symbol. Use the emphasizeRightAngle attribute set to false to negate this default convention. Default = “true”, type = boolean.

Property Example: Attributes as properties

The above listed <angle> attributes are also accessible as properties.

Property Example: Angle, value

The angle and value properties returns the value of the angle in default radians.