1. After checking the solutions to the Lesson Practice from Friday, take a copy of Worksheet 2-5 and complete problems 2, 4, &

2. Lessons 27 & 31: Writing Proofs
Unit 2: Logic & Proof
Lessons 27 & 31: Writing Proofs
Two-Column Proof
Paragraph Proof
Flow Proof

3. Lessons 27 & 31

4. Lessons 27 & 31

5. Lessons 27 & 31

6. Lessons 27 & 31

8. Lessons 27 & 31
We are given that angles 1 and 3 are vertical angles. Since angles 1 and 2 form a linear pair, they are supplementary as are angles 2 and 3. From this it follows that the measures of angles 1 and 2 add up to 180 degrees and angles 2 and 3 will also add up to 180 degrees. By the transitive property of equality, we can establish that the measures of angles 1 and 2 added together will equal the measures of angles 2 and 3 added together. Using the subtraction property, we can deduce that the measure of angle 1 is equal to the measure of angle 3. By the definition of congruence, two angles whose measures are equal are congruent thus angle 1 and angle 3 are congruent.

9. Lessons 27 & 31

10. Lessons 27 & 31
Write a flow proof, a paragraph proof, and a two column proof of this theorem

11. Lessons 27 & 31
Now re-write the proof of the Vertical Angles Theorem using the Congruent Supplements Theorem.

12. Lessons 27 & 31 Classwork: Complete Lesson Practice page 172 problem b
Lesson Practice pages problems a & c
Homework: Worksheet 2-6 problems