Unit 2: Properties of Angles and Triangles

2.2 Angles Formed by Parallel Lines Remember: When a transversal intersects a pair of parallel lines, the corresponding angles that are formed by each parallel line and the transversal are equal Also, vertically opposite angles are equal

There are also other relationships among the measures of the eight angles formed when a transversal intersects two parallel lines. Lets investigate the other angles

Alternate interior angles: two non-adjacent interior angles on opposite sides of a transversal. Non adjacent = not beside each other

Since we know corresponding angles are equal when two parallel lines are intersected by a transversal and vertically opposite angles are equal, make a conjecture about alternate interior angles

Alternate exterior angles: two non-adjacent exterior angles formed between two lines and a transversal, on opposite sides of the transversal.

Since we know corresponding angles are equal when two parallel lines are intersected by a transversal, vertically opposite angles are equal AND alternate interior angles are equal, make a conjecture about alternate exterior angles Let’s prove it!

Make a conjecture Is there a relationship between two interior angles on the same side of the transversal?

Example 2 (p. 76) Using reasoning, determine the measures of a, b, c, and d. Explain WHY!! Use your words!!

Example 3 (p. 77)

Example 20a (p.82)

Key Ideas When a transversal intersects two parallel lines, The corresponding angles are equal The alternate interior angles are equal The alternate exterior angles are equal The interior angles on the same side of the transversal are supplementary (add to 180°)

Need to know If a transversal intersects two lines such that The corresponding angles are equal, or The alternate interior angles are equal, or The alternate exterior angles are equal, or The interior angles on the same side of the transversal are supplementary Then the lines are parallel

Homework P. 78-82 For extra practice for Quiz 2.1 and 2.2 # 1, 2, 3, 4, 8 (the upside down T means perpendicular) 10, 15, 16, 20b For extra practice for Quiz 2.1 and 2.2 Mid chapter review p. 84-85