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1Geometry Lesson: Angle Theorems (Day 2) Aim: Do Now: What are the theorems related to angles? (Day 2) A D Q C B 70º,acute 90º,right 120º,obtuse

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2Geometry Lesson: Angle Theorems (Day 2) Theorem #4: A O B G P H If two angles are straight angles, then they are congruent.

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3Geometry Lesson: Angle Theorems (Day 2) Def: Def: Supplementary Angles are two angles whose measures add up to 180 degrees. A OC 12

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4Geometry Lesson: Angle Theorems (Day 2) Ex: Supplementary Angles 1) A B 130º 50º 2) A B 84º 96 º 3) A B 4) B A

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5Geometry Lesson: Angle Theorems (Day 2) Def: Def: A Linear Pair of angles is two adjacent angles whose union is a straight angle. A O C D O D A O C D Theorem #5: A linear pair of angles is supplementary.

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6Geometry Lesson: Angle Theorems (Day 2) Ex: Supplementary Angles Proof StatementReason 1) 2) 3) 4) 5) 6) 7) Given Def. suppl. angles Substitution Postulate Reflexive Postulate Subtraction Postulate 2 1 3 Given: Prove:

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7Geometry Lesson: Angle Theorems (Day 2) Theorems #6: Theorem #6: Supplements of the same angle, or congruent angles, are congruent. 21 3 4

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8Geometry Lesson: Angle Theorems (Day 2) Ex: Suppl. Angles Proof StatementReason 1) 2) 3) 4) Given Supplements of the same, or congruent angles, are congruent. A X B C D 1 2 3 Given: Prove: Def. Of linear pair A linear pair of angles is supplementary.

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9Geometry Lesson: Angle Theorems (Day 2) Def: Def: A Vertical Pair of angles is two angles in which the sides of one angle are opposite rays to the sides of the other angle. Theorem #7: Vertical angles are congruent. A 4 B C D 1 2 3 When two lines intersect, two pairs of vertical angles are created.

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10Geometry Lesson: Angle Theorems (Day 2) Ex 1,2,3: Compl./Suppl./Vert. Angles : 546 7 AB CD 1) Given: Prove: 2) Given: Prove: A B E D C F 3) Given: Prove: B A C D E

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11Geometry Lesson: Angle Theorems (Day 2) Ex 4, 5: Suppl. Angles 4) Two supplementary angles have measures in the ratio 2:7. Determine the measure of both angles. 5) The measure of an angle is 20 less than 4 times its supplement. Find the measure of the angle and its supplement.

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