1. Bellwork Solve for x & y if m & n are parallel
Clickers
Bellwork
Write the converse of the statement:
If two lines are perpendicular, then they intersect at a right angle
Use the diagram to complete the following
Two Alternate Interior Angles are ________________
Two Corresponding Angles are ___________
Two Consecutive Interior Angles are _____________
Solve for x & y
if m & n are parallel 1 2 3 4 5 6 7 8 n x y 65 55 m

2. Bellwork Write the converse of the statement:
If two lines are perpendicular, then they intersect at a right angle
If two lines are not perpendicular, then they do not intersect at a right angle
If two lines do not intersect at a right angle, then they are not perpendicular
If two lines intersect at a right angle, then they are perpendicular

3. Bellwork Use the diagram to complete the following
Two Alternate Interior Angles are 1 2 3 4 5 6 7 8
4 & 6
4 & 8
1 & 8
4 & 5

4. Bellwork Use the diagram to complete the following
Two Corresponding Angles are 1 2 3 4 5 6 7 8
4 & 6
4 & 8
1 & 8
2 & 5

5. Bellwork Use the diagram to complete the following
Two Consecutive Interior Angles are 1 2 3 4 5 6 7 8
4 & 6
4 & 8
1 & 8
2 & 5

6. Bellwork Solve for x & y, if m & n are parallel 45,55 65, 60 60, 60
90, 45 m

7. Prove Lines are Parallel
Section 3.3

8. The Concept
Yesterday we learned about the Theorems that rule Parallel Lines
Today we’re going to see the converses of these statements and their implications

9. Dilemma Using the ruler, draw this diagram
If I wanted to draw another line parallel to the bottom one, what would I do? θ θ
Axis of symmetry
Vertex

10. The Converses
We can use the converse of the theorems that we learned yesterday to prove that two lines are in fact parallel
We do this by setting up our equations like normal, but instead of assuming parallel lines, we find the values that make things parallel
What value of x makes these two lines parallel?
5x-25
145
Axis of symmetry
Vertex

11. Converse Postulates & Theorems
Postulate 16: Corresponding Angles Converse
If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel
Theorem 3.4: Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel
Theorem 3.5: Alternate Exterior Angles Converse
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel
Theorem 3.6: Consecutive Interior Angles Converse
If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel
Postulate 15: Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Theorem 3.1: Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Theorem 3.2: Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
Theorem 3.3: Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
Vertex

12. In Use 25 30 50 Solve for x, given lines a & b are parallel 6x a b 150
Axis of symmetry
Vertex

13. In Use 25 27 54 What value of x makes lines a and b parallel? 2x-4 a b50
Axis of symmetry
Vertex

14. In Use 3.5 10 13 What value of x makes lines a and b parallel? 2x+10 a
Axis of symmetry
Vertex

15. In Use 55 125 18 What value of x, will make lines a and b parallel a x
Axis of symmetry
Vertex

16. In Use 5 28 140 What value of x, will make lines a and b parallel a 5x
Axis of symmetry
Vertex

17. In Use 20 30 60 What value of x, will make lines a and b parallel 60 a
Axis of symmetry
Vertex

18. In Use 5 20 40 What value of x, will make lines a and b parallel a 4x
160 b
Axis of symmetry
Vertex

19. Definition
Before we go too much further we need to discuss the Law of Syllogism within a geometric context
Transitive Property
A similarity between two items can be transferred to the third, if that same similarity is shared with the last two items
e.g.
Axis of symmetry
Vertex

20. Another one Without looking:
What does the transitive property of parallel lines mean? A B C
Theorem 3.7 Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other
Axis of symmetry
Vertex

21. In Use
What is the value of x, a & b are parallel and b &c are parallel a 5x 9 27 45 b
135 c
Axis of symmetry
Vertex

22. Homework
3.3
1, 2, 5-9, even, 40-44

23. Most Important Points Terminology for lines cut by a transversal
Theorems regarding parallel lines cut by a transversal