Unit 2: Properties of Angles and Triangles
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
2.1 Exploring Parallel Lines What are parallel lines? Lines that will never intersect
Explore (p.70)
Transversal: A line that intersects two or more other lines at distinct points. How many different angles do we get in this picture?
Interior angles: any angles formed by a transversal and two parallel lines that lie inside the parallel lines
Exterior angles: any angles formed by a transversal and two parallel lines that lie outside the parallel lines
Corresponding angles: one interior angle and one exterior angle that are non-adjacent and on the same side of a transversal
What do you notice about the angles formed when a transversal intersects parallel lines? Make a conjecture!
Use the relationships you observed to predict the measures of as many of the angles a to g in this diagram as you can.
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
Need to know When a transversal intersects a pair of non-parallel lines, the corresponding angles are not equal
Example Find the value(s) of the missing angle(s) assuming they’re parallel lines 125°
Example Find the values of a assuming they’re parallel lines 2a 4a
Example Find the values of a, b, and c assuming they’re parallel lines
Homework P. 72 # 2, 3, 4, 5, 6