1. Unit 2: Properties of Angles and Triangles

2. Learning Goals You will be able to develop your spatial sense by:
Proving properties of angles formed by intersecting lines
Proving properties of angles in triangles and other polygons
Using proven properties to solve geometric problems

3. 2.1 Exploring Parallel Lines
What are parallel lines?
Lines that will never intersect

4. Explore (p.70)

5. Transversal: A line that intersects two or more other lines at distinct points.
How many different angles do we get in this picture?

6. Interior angles: any angles formed by a transversal and two parallel lines that lie inside the parallel lines

7. Exterior angles: any angles formed by a transversal and two parallel lines that lie outside the parallel lines

8. Corresponding angles: one interior angle and one exterior angle that are non-adjacent and on the same side of a transversal

9. What do you notice about the angles formed when a transversal intersects parallel lines? Make a conjecture!

10. Use the relationships you observed to predict the measures of as many of the angles a to g in this diagram as you can.

11. Key Ideas
When a transversal intersects a pair of parallel lines, the corresponding angles that are formed by each parallel line and the transversal are equal

12. Need to know
When a transversal intersects a pair of non-parallel lines, the corresponding angles are not equal

13. Example
Find the value(s) of the missing angle(s) assuming they’re parallel lines
125°

14. Example
Find the values of a assuming they’re parallel lines 2a 4a

15. Example Find the values of a, b, and c assuming they’re parallel lines

16. Homework
P. 72
# 2, 3, 4, 5, 6