Section 2-5: Proving Angles Congruent

```Section 2-5: Proving Angles
Congruent
Goal 2.02: Apply properties,
definitions, and theorems of angles and
lines to solve problems and write
proofs.
Properties from Algebra
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
equality
10. transitive
11. subtraction
property of equality
Justify the Statement Homework
1. definition of midpoint
2. definition of angle bisector
3. Angle Bisector Theorem
5. definition of midpoint
6. Midpoint Theorem
9. definition of angle bisector
Warm up
• Lesson Quiz 2-4
• Checkpoint quiz p 88 (1-10)
• Mixed Review: p 87 (38 – 44)
Essential Questions
1. How are vertical, complementary, and
supplementary angles identified?
2. What are the theorems about angles?
3. How are they applied?
Two angles side by side with a common vertex
and common side. ( no common interior
points and can’t overlap)
ex. 1
ex. 2
Vertical Angles
a. two angles whose sides form two pairs of
opposite rays.
b. when two lines intersect two pairs of vertical
angles are formed.
Complementary Angles
two angles whose measures have the sum 90.
Each angle is a complement of the other.
x = angle
ex. 1
90 – x = complement
ex. 2
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
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.
Examples p 100 (1-5)
1.
2.
3.
4.
5.
Supplementary to AOD
Supplementary to EOA
Complementary to EOD
A pair of vertical angles
P 100 (10 -18)
10. J = D
11. JAC = DAC
12. JAE and EAF are adjacent & supplementary
13. m JCA = m DCA
14. m JCA + m ACD = 180
16. C is the midpoint of JD
17. EAF and JAD are vertical angles
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 .)
12.All right angles are congruent.
13. If two lines are perpendicular, then they
14. If two lines form congruent, adjacent
angles, then the lines are perpendicular.
15.If the exterior sides of two adjacent acute
angles are perpendicular, then the angles are
complementary.
Together: P 102 (39 – 53 odds, 57, 59)
39.
41.
43.
47. A and B are complementary:
m A = 3x + 12 and B = 2x – 22
49. A is twice as large as its complement, B
51. 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.
57.
59.
Groups of 2 to 3: Do p 102: 40 – 54 even, 58
Individual Practice
• Worksheet: Practice 2-5
Assessment
Standardized Test Prep: p 103 (60 – 66)
Homework
Worksheets:
Proving Theorems
Perpendicular Lines
Study definitions,
postulates and theorems
for Multiple choice test
Wednesday
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