another geo proof

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another geo proof

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Aim: : 

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

Theorem #4: : 

2 Geometry Lesson: Angle Theorems (Day 2) Theorem #4: If two angles are straight angles, then they are congruent.

Def: : 

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

Ex: Supplementary Angles : 

4 Geometry Lesson: Angle Theorems (Day 2) Ex: Supplementary Angles 50º 96 º

Def: : 

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

Ex: Supplementary Angles Proof : 

6 Geometry Lesson: Angle Theorems (Day 2) Ex: Supplementary Angles Proof Given Given Def. suppl. angles Def. suppl. angles Substitution Postulate Reflexive Postulate Subtraction Postulate

Theorems #6: : 

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

Ex: Suppl. Angles Proof : 

8 Geometry Lesson: Angle Theorems (Day 2) Ex: Suppl. Angles Proof Given Supplements of the same, or congruent angles, are congruent. Def. Of linear pair A linear pair of angles is supplementary.

Def: : 

9 Geometry 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.

Ex 1,2,3: Compl./Suppl./Vert. Angles: : 

10 Geometry Lesson: Angle Theorems (Day 2) Ex 1,2,3: Compl./Suppl./Vert. Angles:

Ex 4, 5: Suppl. Angles : 

11 Geometry 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.