Download Angles - Math with Ms. Newman

EOC Warm-Up #2
Thursday – September 4, 2008
H.W. #8 Due TODAY
 New EOC Review sheets are on your desk!

Just write your answer, but make sure you write the
page # and problem #’s.
Workbook page 19
#’s 1-5
Brief review from yesterday…
Reteaching 2.3, pg. 19
Can I use the Law of Detachment?
If a person goes to the zoo, then he or she will see animals.
 Karla goes to the zoo.
If a person goes to the zoo, then he or she will see animals.
 Karla sees animals.
Brief review from yesterday…
Reteaching 2.3, pg. 19
Can I use the Law of Syllogism?

If a polygon is a hexagon, then the sum of its angles is 720.

If the sum of the angles of a polygon is 720, then it has six sides.
If a polygon is a hexagon, then it has six sides.
H.W. Solutions
pg. 20 #3, 6, 9, 12
3.
Triangle DEF is a right triangle.
6.
If you vacation at the beach, then you like Florida.
9.
Not possible
12.
On Thursday, the track team warms up by jogging
2 miles.
H.W.
pg. 20 #’s 9 and 12
9.
If two figures are congruent, their areas are equal.
The area of ABCD equals the area of PQRS.
12. If it does not rain, the track team will have practice.
If the track team has practice, the team members will
warm up by jogging 2 miles.
It does not rain Thursday!
Proving Angles Congruent
Ch. 2.5
Today’s GOALS
By the end of class today, YOU should be able to…
1. Identify angle pairs.
2. To prove and apply
theorems about angles.
Vertical Angles


Two angles whose sides form two pairs of
opposite rays
They are across from one another.
Vertical Angle Theorem

Vertical angles are congruent (  ).
Adjacent Angles


Two coplanar angles with a common side,
common vertex, and no common interior points.
They are next to each other.
Complementary Angles


Two angles whose measures have sum 90.
Each angle is called the complement of
the other.
Supplementary Angles


Two angles whose measures have sum 180.
Each angle is called the supplement of the
other.
Theorem

A proven fact.

Theorem: All right angles are congruent.

Theorem: If two angles are congruent and
supplementary, then each is a right angle.
Linear Pair

Two angles that form a line.
Ex.1: Identifying Angle Pairs
a) Complementary
b) Supplementary
c) Vertical
Ex.2:
What can you conclude from the
information in the diagram?
a)
b)
1 and 2 are:
2 and 3 are:
c)
d)
4 and 5 are:
1 and 4 are:
Ex.3:
Name an angle or angles in the
diagram described by each of the following:
1. supplementary to AOD
2. adjacent and congruent to AOE
3. supplementary to EOA
4. complementary to EOD
5. a pair of vertical angles
Ex.4: Write an equation, then solve.
a.
3x
b.
(80 – x)
(4x + 5)
(3x + 8)
Ex.4 cont…
c.
d.
54
4x
(12x – 15)
(3x + 45)
Ex.4 cont…
e.
g.
3x
(85 – x)
(3x + 8)
(5x + 4y)
f.
y
3x
75
(5x – 20)
Homework #10

P. 100-102: 2-34 evens; 50, 51, 52
Cooldown
Use your notes NOT your neighbor!
1.
2.
3.
4.
5.
Today’s EOC Warm-Up, the answer to #4
Are all right angles congruent?
Ex.1 (b) answer
Ex.3 (c) answer
Ex.4 (c) equation and answer