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Transcript
September 06, 2013 Geometry Unit A: Basics of Geometry Notes Day 7 Objectives: *Identify types of angles including linear pair, supplements, complements, vertical, adjacent to prove and apply theorems about angles *Understand and use the definition of transversal and identify types of angles including alternate interior, alternate exterior, same-side interior, same-side exterior and corresponding to prove and apply theorems about angles *Prove and use properties of parallel lines cut by a transversal Assignment: Worksheet 7 Remember this Vocabulary? Vertical Angles Adjacent Angles Complementary Angles Supplementary Angles Ex 1 Identifying Angle Pairs In the diagram identify pairs of numbered angles that are related in the following ways: 1. Complementary 2. Supplementary 3. Vertical 4. Adjacent September 06, 2013 What can you conclude from a drawing? What can you NOT conclude from a drawing? Ex 2 Making Conclusions From a Diagram September 06, 2013 Useful Theorem: Vertical Angles Theorem-Vertical angles are congruent Ex 3 Practice with proofs and plans. Prove Alternate Interior Angles Theorem Ex 4 Prove Same-Side Interior Angles Theorem September 06, 2013 15 14 5 0° 12 77 11 4 10 9 3 7 6 2 5 4 1 2 0 49° 0 1 3 8 13 September 06, 2013 15 14 13 5 12 11 237 4 10 9 8 3 7 6 2 5 4 3 1 2 1 90° 0 0 0° September 06, 2013 September 06, 2013 Ex 5 Practice with Proofs and Plans More Useful Theorems: Congruent Supplements Theorem-If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Congruent Complements Theorem- If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. Right Angles Theorem-All right angles are congruent. Theorem-If two angles are congruent and supplementary, then each is a right angle. September 06, 2013 Ex 6 Comparing Types of Proofs September 06, 2013 Ex 7 Practicing Proofs-Prove the Congruent Complements Theorem Even More Useful Theorems: Theorem-If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Theorem-If two sides of two adjacent acute angles are perpendicular, th en the angles are complementary. Theorem-If two lines are perpendicular, then they intersect to form four right angles. Theorem- If two lines are parallel to the same line, then they are parallel to each other. Theorem- In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. September 06, 2013 Ex 8 Practicing Proofs…One more flow September 06, 2013 0° 211 September 06, 2013 113 0° September 06, 2013