1. Section 2-5: Proving Angles Congruent
Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

2. Homework Answers 1. addition property of equality
Properties from Algebra
1. addition property of equality
2. division property of equality
3. multiplication property of equality
4. subtraction property of equality
5. division property of equality
6. distributive
7. transitive
8. symmetric 9. addition property of equality 10. transitive 11. subtraction property of equality

3. Justify the Statement Homework
1. definition of midpoint
2. definition of angle bisector
3. Angle Bisector Theorem
4. Angle Addition Postulate
5. definition of midpoint
6. Midpoint Theorem
7. Angle Addition Postulate
8. Segment Addition Postulate
9. definition of angle bisector

4. Warm up Lesson Quiz 2-4 Checkpoint quiz p 88 (1-10)
Mixed Review: p 87 (38 – 44)

5. Essential Questions
How are vertical, complementary, and supplementary angles identified?
What are the theorems about angles?
3. How are they applied?

6. What are adjacent angles?
Two angles side by side with a common vertex and common side. ( no common interior points and can’t overlap) ex. 1 ex. 2

7. Vertical Angles
two angles whose sides form two pairs of opposite rays.
when two lines intersect two pairs of vertical angles are formed.

8. Complementary Angles
two angles whose measures have the sum 90. Each angle is a complement of the other. x = angle 90 – x = complement ex. 1 ex. 2

9. Supplementary Angles
two angles whose measures have the sum 180. Each angle is a supplement of the other. x = angle 180 – x = supplement ex. 1 ex. 2

10. Reminders
Complementary and supplementary angles do not have to be adjacent angles.
Complementary will always be only 2 angles whose sum is 90.
Supplementary must always be 2 angles whose sum is 180.

11. Examples p 100 (1-5) Supplementary to AOD
Adjacent and congruent to AOE
Supplementary to EOA
Complementary to EOD
A pair of vertical angles

12. P 100 (10 -18)
J = D
JAC = DAC
JAE and EAF are adjacent & supplementary
m JCA = m DCA
m JCA + m ACD = 180
AJ = AD
C is the midpoint of JD
EAF and JAD are vertical angles
AC bisects JAD

13. Theorems
9. Vertical angles are congruent. 10. If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. (Supplements of the same/  angles are .) 11. If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. (Complements of the same/ angles are .)

14. All right angles are congruent.
If two lines are perpendicular, then they form congruent, adjacent angles.
If two lines form congruent, adjacent angles, then the lines are perpendicular.
If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

15. Together: P 102 (39 – 53 odds, 57, 59)
39.
41.
43.
45. Congruent adjacent complementary angles
A and B are complementary:
m A = 3x + 12 and B = 2x – 22
A is twice as large as its complement, B
A is twice as large as its supplement, B
53. The measure of B, complement of A, if 4 times the measure of C, complement of A.

16. 57. 59. Groups of 2 to 3: Do p 102: 40 – 54 even, 58

17. Individual Practice
Worksheet: Practice 2-5

18. Assessment
Standardized Test Prep: p 103 (60 – 66)

19. Homework
Worksheets: Proving Theorems Perpendicular Lines Study definitions, postulates and theorems for Multiple choice test Wednesday