A [b]linear pair[/b] is defined as angles having a common side, and whose noncommon sides form opposite rays. In the diagram above, Angle 1 and Angle 2 form a linear pair. When angles share a common side, they are [i]adjacent.[/i]
Lines and Angles (Module 4)
G-CO.3.9
[size=85]This activity gives students the opportunity to observe[/size] theorems [which] include: [i]Vertical angles are congruent; [i]when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are [exactly those] equidistant from the segment’s endpoints.[/i][/i]
REMEMBER:
[b]Complementary angles[/b] are angles whose measures have a sum of 90 degrees.[br][b]Supplementary angles[/b] are angles whose measures have a sum of 180 degrees.
DEFINITION
In this diagram, which ray is the common side for the adjacent angles [math]\angle1[/math] and [math]\angle2[/math] ?
In the diagram below, click and drag points A and C to change the measures of the angles.
What do you notice is always true about the linear pair of angles?
DEFINITION
[b]Vertical angles[/b] - [i]non[/i]adjacent angles formed by two intersecting lines. (Read: vertical angles do [b]not[/b] have a common side)
In the diagram below, click and drag points A and C to change the measures of the angles.
What do you notice is always true about the vertical angles?
In the diagram above, which angles are vertical angles?
Note the kinds of angles formed by 2 lines p and q, and transversal t. This diagram is also in your text (p. 175).
Here the two lines cut by a transversal are parallel. Click and drag point B to change the angle measures. Answer the questions below about what is ALWAYS true about these special angles when parallel lines are cut by a transversal.
Same-Side Interior Angles Postulate
If two parallel lines are cut by a transversal, then the same-side interior angles (like Angle Two and Angle Three) are
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the corresponding angles (like Angle One and Angle Four) are
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the alternate interior angles (like Angle One and Angle 3) are
What is line CD?
In the diagram below, which of the following provides the [b]best[/b] description of line CD as it relates to segment AB?
Perpendicular Lines
Click and drag point D.
While the lengths are changing, is there anything that is always true?