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Day 4 ­ Section 2.5.notebook
October 06, 2014
Day 4­ 2.5 Proving Angles Congruent
Objectives: To identify angle pairs To prove and apply theorems about angles G.1.A, M.2.B
Performance Standard 1.8, 3.5, 4.1 DOK­1, 2
Knowledge MA 2, MA 1
Day 4 ­ Section 2.5.notebook
October 06, 2014
Vertical Angles: "across from each other"
2
3
1
4
Vertical Angles are congruent. How should we code them? 2
Day 4 ­ Section 2.5.notebook
October 06, 2014
Name the vertical angles below: D
A
C
B
E
3
Day 4 ­ Section 2.5.notebook
October 06, 2014
Adjacent angles: 1) Share an entire side
2) Share a vertex
3) Do NOT overlap!
D
C
E
F
O
B
A
Identify adjacent angles in the diagram above
4
Day 4 ­ Section 2.5.notebook
October 06, 2014
Ex 1) Are these angles adjacent? Why or why not??
B
A
<AOB and <BOC
C
O
S
R
W
<RXS and <SWT
T
X
5
Day 4 ­ Section 2.5.notebook
P
N
October 06, 2014
<NPM and <QNP
M
Q
V
<ESV and <VSD
E
S
D
6
Day 4 ­ Section 2.5.notebook
October 06, 2014
Complementary Angles: add up to 90 degrees. 30
2
60
1
Supplementary Angles: add up to 180 degrees.
120
60
Linear Pairs are SUPPLEMENTARY!
7
Day 4 ­ Section 2.5.notebook
October 06, 2014
Z
Examples:
<XAY =
________
X
P
45o
A
<ZAP and ______________ are supplementary
Y
<XAY and _______________ are complementary
M
<ZAX and ______________________ are vertical. m<PAZ = _____________________
8
Day 4 ­ Section 2.5.notebook
October 06, 2014
Assignment ­ portions taken from pg 100 of Geometry textbook
Name: ________________________________________________________ Date: ____________________________ Block: _________
Section 2.5 ­ Proving Angles Congruent and Angle Relationships
For #1­5, name an angle or angles in the diagram described by each of the following:
1. supplementary to <AOD
A
E
3. supplementary to <EOA
60o
4. complementary to <EOD
D
5. two pairs of vertical angles
6. What is the measure of <DOC?
B
2. adjacent and congruent to <AOE
O
C
7. What is the measure of <COB?
8. What is the measure of <EOB? Each conditional statement below is true. b) Is the converse true or false? a) Write the converse.
c) If the converse is false, provide a counterexample. 9. If y + 7 = 32, then y = 25. a)
b)
c) 10. If you live in Australia, then you live south of the equator.
a)
b)
c) 9
Day 4 ­ Section 2.5.notebook
October 06, 2014
11. If n > 0, then n2 > 0.
a)
b)
c)
2
12. Solve: x ­ 4 = ­8
7
13. Write the equation of the line shown on the graph in slope­intercept form. 14. Re­write the following sentence as a conditional statement:
All of the trees in Redwood National Forest are beautiful. 10