Geometry 3.1 Brett Solberg AHS ’11-’12

Warm-up Use the vertical angles theorem to solve for x. Pick up a green notes packet for chapter 3 from the back table.

Real Salt Lake 11 players Goalkeeper GK Defender D Midfielder M Forward F

Geometric Application Angles in certain positions have special properties. Transversal: a line that intersects two lines. A transversal creates 8 angles. 1 2 4 3 5 6 8 7

Interior Angles Interior 1 2 4 3 5 6 8 7 1 2 4 3 5 6 8 7 Interior ∠3, ∠4, ∠5, ∠6 are interior angles.

Exterior Angles ∠1, ∠2, ∠7, and ∠8 are exterior angles

Alternate Interior Angles 1 2 4 3 5 6 8 7 ∠3 and ∠5 are alternate interior angles. ∠4 and ∠6 are alternate interior angles.

Corresponding angles 1 2 4 3 5 6 8 7 ∠1 and ∠5 are corresponding angles. ∠2 and ∠6 are corresponding angles. ∠3 and ∠7 are corresponding angles. ∠4 and ∠8 are corresponding angles.

Same-side Interior Angles 1 2 4 3 5 6 8 7 ∠3 and ∠6 are same-side interior angles. ∠4 and ∠5 are same-side interior angles.

Alternate Exterior Angles ∠1 and ∠7 are alternate exterior angles. ∠2 and ∠8 are alternate exterior angles.

Postulate 3-1 If a transversal intersect two parallel lines, then corresponding angles are congruent. 1 2 ∠1 ≅ ∠2

Theorem 3-1 If a transversal intersect two parallel lines, then alternate interior angles are congruent. 1 2 ∠1 ≅ ∠2

Theorem 3-2 If a transversal intersect two parallel lines, then same-side interior angles are supplementary. 1 2 ∠1 + ∠2 = 180

Theorem 3-3 If a transversal intersect two parallel lines, then alternate exterior angles are congruent. 1 2 ∠1 ≅ ∠2

Theorem 3-4 If a transversal intersect two parallel lines, then same-side exterior angles are supplementary. 1 2 ∠1 + ∠2 = 180

Example 3 Find the m∠1 and m ∠2. Justify your answer. 42 2 1

Example 4 Find a, b, c. Justify your answers. a c b 40 65

Find x, y, and the measure of all angles.

Homework 3.1 Worksheet