Objectives: Identify the properties of adjacent angles.

1. 2.5 Adjacent & Vertical Angles Objectives: Identify the properties of adjacent angles. Recognize congruency between vertical angles. Warm-Up: Shadow was examining an angle measuring 14 ½ degrees, using his magnifying glass that magnifieseverything two times. Under the glass how large would that angle measure?

2. Adjacent Angles: Two angles in a plane that share a common vertex and a common side but have no interior points in common,

3. Example: Name all of the pairs of adjacent angles in the figure. X Y W V Z

4. Examples: Explain why the indicated angles are NOT adjacent. 2 < 1 & < 3 3 1 1 2 < 1 & < 2 A B 2 1 C < 1 & < 2 < ADB& < ADC

5. Vertical Angles: The opposite angles formed by two intersecting lines.

6. Vertical Angle Theorem: If two angles form a pair of vertical angles, then they are congruent.

7. Example: Refer to the diagram below which consists of three intersecting lines. Tell which angle is congruent to the given angle. I P L S E F D < LEI ___ < SEF ___ < PED

8. Example: For each pair of intersecting lines, find m<ABC C A D B E

9. Example: For each pair of intersecting lines, find m<ABC A E B D C

10. Example: For each pair of intersecting lines, find m<ABC A B C E D

11. Example: For each pair of intersecting lines, find m<ABC A C B E D

12. Example: For each pair of intersecting lines, find m<ABC E A B C D

13. Example: For each pair of intersecting lines, find m<ABC E D B C A

14. Example: For each pair of intersecting lines, find m<ABC A B E C D

15. Example: For each pair of intersecting lines, find m<ABC S R A B P Q C

16. Inductive Reasoning: The process of forming conjectures that are based on observations.

17. Logical Chain: A series of logically linked conditional statements. Arrange the three statements below into a logical chain. If I go shopping I will buy a new umbrella. If it rains Saturday then I am going shopping. If I buy a new umbrella then I won’t get wet.