Angle Pairs
1.
and
are lines that intersect at . Estimate the measures of angles
and
the diagram without using a protractor. Share your estimate with a partner and revise if
needed.
2. Use a protractor to measure angles
sum of your two estimates accurate?
3. Find the measure of angle
4. Find and label a second
angle
.
and
in
. How close were your estimates? Was the
. Explain or show your reasoning.
degree angle in the diagram. Find and label an angle congruent to
5. Sketch a diagram that shows two angles that are both congruent to each other and
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles
complementary. What are their angle measures?
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles
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
Lines
and
are parallel.
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles
in the second diagram.
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
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles
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?
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles
Alternate Interior Angles are Congruent
Suppose
and
are parallel lines. The point
is on , and the point
is on , as shown in the
diagram.
is the midpoint of segment
, which is contained in line , which is a transversal line to
and
.
1. Find a rigid transformation showing that angles
2. In this picture, lines
and
are no longer parallel.
and
are congruent.
is still the midpoint of segment
Does your argument in the previous problem apply in this situation? Explain.
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles
.
Are you ready for more?
In the diagram, lines
and
are parallel. Find the angle measures of all the missing angles
labeled with a '?'.
Unit 3: Rigid Transformations and Congruence Lesson 11: Alternate Interior Angles