Sec 2 Hon – Notes 2.4, 2.5 (Carnegie)
2.4: Pg 176 Use a protractor to carefully measure each of the numbered angles below. Work with your partner.
Ask questions and compare measurements. Be prepared to share your results with the class.
Corresponding Angle Postulate: If two parallel lines are intersected by a transversal, then the corresponding
angles are congruent.” Circle a pair of corresponding angles in the diagram.
1. Name all pairs of angles above that are congruent using the Corresponding Angle Postulate.
2. Pg 178 The Alternate Interior Angle Conjecture states: “If two parallel lines are intersected by a transversal,
then alternate interior angles are congruent.”
As a class we will use the Vertical Angle Theorem and the Corresponding Angle Postulate to complete a proof of
the Alternate Interior Angle conjecture. We will make a plan before we start writing! There are a variety of
possible ways to prove this theorem!
Given: w ∥ x, and z is a transversal
Prove: ∠3 ≅ ∠6 (Alternate Interior Angles)
STATEMENTS
REASONS
1.
1.
2.
2.
3.
3.
4.
4.
Discuss other possible methods of completing this proof.
3. Pg 176 Use your diagram at the top of this page as we review the names of different angle pairs. Record
“congruent” or “supplementary” next to the angle pair names, based on your measurements.
If the lines are parallel, then…
Alternate Interior Angles are:
Alternate Exterior Angles are:
Same Side Interior Angles are:
Same Side Exterior Angles are:
Vertical Angles are:
Corresponding Angles are:
4. Pg 180 #2 Complete the Alternate Exterior Angle proof below with your partner. You may use any Theorem
we have already proved or any postulate we have already stated. Be prepared to share with the class!
Given: w ∥ x, and z is a transversal
Prove: ∠1 ≅ ∠8 (Alternate Exterior Angles)
STATEMENTS
1.
2.
3.
4.
REASONS
1.
2.
3.
4.
5. Pg 181 #3 Complete the “blanks” in the “big ideas” Same-Side Interior Angle proof below with your partner.
You may use any Theorem we have already proved or any postulate we have already stated. Be prepared to
share with the class!
Given: w ∥ x, and z is a transversal
Prove: ∠4 𝑎𝑛𝑑 ∠6 are supplementary
STATEMENTS
REASONS
1.
1.
2. ∠2 ≅ ∠6
2.
3. ?
+
? = 180°
3. linear pairs are supplementary
4.
4.
5.
5.
As similar proof could be used to prove that same-side exterior angles are supplementary also.
6. Pg 183 Complete the following problem.
Summary of what we learned in section 2.4:
Corresponding Angle Postulate: If two parallel lines are intersected by a transversal, then the corresponding
angles are congruent.
Alternate Interior Angle Theorem: If two parallel lines are intersected by a transversal, then the alternate interior
angles are congruent.
Alternate Exterior Angles Theorem: If two parallel lines are intersected by a transversal, then the alternate
exterior angles are congruent.
Same-Side Interior Angle Theorem: If two parallel lines are intersected by a transversal, then interior angles on
the same side of the transversal are supplementary.
Same-Side Exterior Angle Theorem: If two parallel lines are intersected by a transversal, then exterior angles on
the same side of the transversal are supplementary.
2.5: Converse of Theorems from 2.4
What is a converse?
The converse of each of the theorems/postulates above could be proven.
Write the converse of the Alternate Interior Angle Theorem:
Pg 192 Use the diagram to answer the questions. Do #1-5 with a partner then do #6-10 on your own.
1.
2.
3.
4.
5.
What theorem or postulate would use ∠2 ≅ ∠7 to justify line p is parallel to line r?
What theorem or postulate would use ∠4 ≅ ∠5 to justify line p is parallel to line r?
What theorem or postulate would use ∠1 ≅ ∠5 to justify line p is parallel to line r?
What theorem or postulate would use 𝑚∠4 + 𝑚∠6 = 180° to justify line p is parallel to line r?
What theorem or postulate would use 𝑚∠1 + 𝑚∠7 = 180° to justify line p is parallel to line r?
6.
7.
8.
9.
10.
Which theorem or postulate would use line p is parallel to line r to justify ∠2 ≅ ∠7?
Which theorem or postulate would use line p is parallel to line r to justify ∠4 ≅ ∠5?
Which theorem or postulate would use line p is parallel to line r to justify ∠1 ≅ ∠5?
Which theorem or postulate would use line p is parallel to line r to justify 𝑚∠4 + 𝑚∠6 = 180°?
Which theorem or postulate would use line p is parallel to line r to justify 𝑚∠1 + 𝑚∠7 = 180°?