1. 3.1 – Identify pairs of lines and Angles
Geometry Chapter 3
3.1 – Identify pairs of lines and Angles

2. Warm-Up 1.) Parallel Lines 2.) Skew Lines 3.) Parallel Planes
Using your own knowledge, or by using your Chromebooks, find the definitions of these terms.
1.) Parallel Lines
2.) Skew Lines
3.) Parallel Planes

3. Identify Pairs of Lines and Angles
Objective: Students will be able to identify angle pairs formed by intersecting lines.
Agenda
Parallel/Perpendicular Lines
Transversals (w/Angles)
Examples

4. Vocabulary – Parallel Lines
Definition: Lines that are coplanar and do not intersect.
Picture: 𝒎 𝒏
Notation:
𝒎∥ 𝒏
Knowledge Connection:
What examples of parallel lines are there in the real world?

5. Vocabulary – Skew Lines
Definition: Lines that are not coplanar and do not intersect.
Picture: 𝒎 𝒌
Knowledge Connection:
What examples of skew lines are there in the real world.

6. Vocabulary – Parallel Planes
Definition: Planes that do not intersect.
Picture:
Notation:
𝑷𝒍𝒂𝒏𝒆 𝑨∥ 𝑷𝒍𝒂𝒏𝒆 𝑩 𝑨 𝑩
Knowledge Connection:
What examples of parallel lines are there in the real world.

7. For the Postulates List
Postulate 13: The Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point that is parallel to the given line.
Picture 𝑷 𝒔 𝒓

8. For the Postulates List
Postulate 14: The Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point that is perpendicular to the given line.
Picture 𝒓 𝑷 𝒔

9. Vocabulary - Transversal
Definition: A transversal is a line that intersects two or more coplanar lines at different points.
Picture:
Line 𝒕 is the transversal of lines 𝒎 and 𝒏 𝒕 𝒎 𝒏
Knowledge Connection:
What examples of transversals are there in the real world?

10. Vocabulary – corresponding angles
Definition: Angles that have corresponding positions.
Picture:
Knowledge Connection:
What does it mean to have corresponding positions? 1 2
<1 and <2 are corresponding angles

11. Vocabulary – alternate interior angles
Definition: Angles that lie between the two lines, and are on opposite sides of the transversal.
Picture:
Knowledge Connection:
What does it mean to alternate? To be in the interior? 3 4
<3 and <4 are alternate interior angles

12. Vocabulary – alternate exterior angles
Definition: Angles that lie outside the two lines, and are on opposite sides of the transversal.
Picture:
Knowledge Connection:
What does it mean to alternate? To be in the exterior? 5 6
<5 and <6 are alternate exterior angles

13. Vocabulary – consecutive interior angles
Definition: Angles that lie between the two lines, but are on the same side of the transversal.
Picture:
Knowledge Connection:
What does it mean to be consecutive? To be in the interior? 7 8
<7 and <8 are consecutive interior angles

14. Practice – Identify Angle Relationships
Classify the pair of numbered angles 5 1
Corresponding Angles

15. Practice – Identify Angle Relationships
Classify the pair of numbered angles 6 4
Consecutive Interior Angles

16. Practice – Identify Angle Relationships
Classify the pair of numbered angles 8 3
Alternate Interior Angles

17. Practice – Identify Angle Relationships
Classify the pair of numbered angles 7 2
Alternate Exterior Angles

18. Practice – Identify Angle Relationships
Identify the following pairs from the given diagram
Corresponding Alternate Interior Alternate Exterior Consecutive Interior 7 8 6 5 4 3 2 1
<𝟏 𝒂𝒏𝒅<𝟓
<𝟐 𝒂𝒏𝒅<𝟕
<𝟏 𝒂𝒏𝒅<𝟖
<𝟐 𝒂𝒏𝒅<𝟓
<𝟑 𝒂𝒏𝒅<𝟔
<𝟐 𝒂𝒏𝒅<𝟔
<𝟒 𝒂𝒏𝒅<𝟓
<𝟒 𝒂𝒏𝒅<𝟕
<𝟑 𝒂𝒏𝒅<𝟕
<𝟒 𝒂𝒏𝒅<𝟖

19. Final Practice – Identify Angle Relationships
Using the diagram, identify the type of angles
1.) <1 𝑎𝑛𝑑< ) <4 𝑎𝑛𝑑<7
2.) <3 𝑎𝑛𝑑< ) <8 𝑎𝑛𝑑<13
3.) <7 𝑎𝑛𝑑<15
4.) <1 𝑎𝑛𝑑<16 7 8 6 5 4 3 2 1 15 16 14 13 12 11 10 9