Let's learn what a right angle is first. Right angles are present many places in real life.
Look at the corners of this room or the edges of your books. A right angle is an angle that
measures 90 degrees. A right angle looks like this:
Mentor: The second type of angle is acute. An acute angle is an angle whose measure is between 0 and
90 degrees. An acute angle looks like this:
Student: Let me guess! The third type is an angle whose measure is more than 90 degrees.
Mentor: Yes, an obtuse angle is an angle whose measure is between 90 and 180 degrees. An obtuse angle
looks like this:
Mentor: We also have names for pairs of angles. Angles are formed when lines intersect. We are going
to look at the angles formed when two
parallel lines are intersected by a third line called a
transversal . In this picture, the red lines are parallel and the blue line is the transversal.
Student: Those lines formed 8 angles.
Mentor: Good job. Now, who can show me an acute angle?
Student: I can! It is the one on the top right.
Mentor: Right again. Who can show me an obtuse angle?
Student 2: I think it is the one on the top left.
Mentor: Correct. We need an easier way of referring to the angles we are talking about. So from now
on, we will label our angles. Angles a and b are
Mentor: Angles f and h are also adjacent angles. Does anyone know what it means for a pair of angles
to be adjacent?
Student: Does it mean that they are side by side?
Mentor: Yes, adjacent angles are angles that share a ray. Can anyone tell me another pair of angles
that are adjacent?
Student: Yes, angles c and d are adjacent.
Student 2: I can too; angles b and d are adjacent.
Mentor: Good job, angles c and d are adjacent and so are angles b and d. There are many pairs of
adjacent angles in the picture. Now, let's talk about
vertical angles. Angles a and d are vertical angles.
Mentor: Angles f and g are also vertical angles. Can anyone guess what it means for a pair of angles
to be vertical?
Student: Are vertical angles ones that are opposite from each other?
Mentor: Good job! Vertical angles share only one point. That point is called the vertex. Can anyone
name another pair of vertical angles?
Student 2: I can; angles b and c are vertical angles.
Student: Angles e and h are also vertical angles.
Mentor: Yes, angles b and c are vertical angles and so are angles e and h. Now that we know what
adjacent and vertical angles are, let's talk about
alternate interior angles. Angles c and f are alternate interior angles.
Mentor: Angles d and e are also alternate interior angles. Who knows what it means for two angles to
be alternate interior angles?
Student: Are alternate interior angles the ones that are inside the lines and on opposite sides from
Mentor: Yes, alternate interior angles are angles that are inside the parallel lines and on opposite
sides of the transversal. Now, who thinks they can guess what
alternate exterior angles are?
Student: They are the angles on the outsides of the parallel lines and on opposite sides of the
Mentor: Correct again. Who can give me an example?
Student: Angles a and h are alternate exterior angles.
Student 2: Angles b and g are also alternate exterior angles.