Lesson: Alternate Interior Angles
Activity Statement: Angle Pairs
1.
and
are lines that intersect at
. Estimate the measures of angles
and
in the diagram
without using a protractor. Share your estimate with a partner and revise if needed.
2. Use a protractor to measure angles
two estimates accurate?
3. Find the measure of angle
and
. How close were your estimates? Was the sum of your
. Explain or show your reasoning.
4. Find and label a second
degree angle in the diagram. Find and label an angle congruent to angle
5. Sketch a diagram that shows two angles that are both congruent to each other and complementary. What
are their angle measures?
Activity Statement: Cutting Parallel Lines With a Transversal
Lines
and
are parallel. They are cut by transversal
.
.
1. Work with your partner to find the seven unknown angle measures in the diagram. Explain your reasoning.
2. What do you notice about the eight angles at points
and
?
3. Using what you noticed, find the measures of the four angles at point
and
are parallel.
in the second diagram. Lines
4. The next diagram resembles the first one but the lines form slightly different angles. Work with your partner
to find the 6 unknown angles with vertices at points and .
5. What do you notice about the angles in this diagram as compared to the previous diagram? How are the two
diagrams different? How are they the same?
Activity Statement: Alternate Interior Angles are Congruent
Suppose
and
are parallel lines. The point
is the midpoint of segment
is on , and the point
, which is contained in line , which is a transversal line to
1. Find a rigid transformation showing that angles
2. In this picture, lines
and
is on , as shown in the diagram.
are no longer parallel.
and
and .
are congruent.
is still the midpoint of segment
.
Does your argument in the previous problem apply in this situation? Explain.
Activity Statement: All The Rest
The diagram shows two parallel lines cut by a transversal. One angle measure is shown.
Find the values of , , , , ,
and .