warm-up: billiards (“pool”)
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Warm-Up: Billiards (“Pool”). Who has played pool? What’s a “bank shot”? How do you know where to hit the ball on the side? It’s all in the angles! Angles are the foundation of geometry. 1.4 Angles & their Measures. Objectives: Define: Angle, side, vertex, measure, degree, congruent - PowerPoint PPT PresentationTRANSCRIPT
Warm-Up: Billiards (“Pool”)
• Who has played pool?• What’s a “bank shot”?• How do you know
where to hit the ball on• the side?• It’s all in the angles!• Angles are the
foundation of geometry
1.4 Angles & their MeasuresObjectives:
•Define: Angle, side, vertex, measure, degree, congruent•Name angles with the vertex always in the middle•Measure angles with a protractor•Identify congruent angles•Classify angles as acute, right, obtuse, or straight•Add and subtract angle measures using the angle addition postulate
Angle symbol:
• 2 rays that share the same endpoint (or initial point)
Y
Z
X
Sides – the rays XY & XZ
Vertex – the common endpoint; X
Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram).
Angles can also be named by a #. (<5)
5
In the figure, there are three different <Q’s (two smaller ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name
Postulate 3: Protractor Post.• The rays of an angle
can be matched up with real #s (from 1 to 180) on a protractor so that the measure of the < equals the absolute value of the difference of the 2 #s.
55o
20o
m<A = 55-20
= 35o
Interior or Exterior?
• B is ___________• C is ___________• D is ___________
in the interior
in the exterioron the <
A
B
C
D
Adjacent Angles
• 2 angles that share a common vertex & side, but have no common interior parts.
(they have the same vertex, but don’t overlap) such as <1 & <2
12
Example 3:.
Q
P S
R
If m<QRP=5xo, m<PRS=2xo, & m<QRS=84o, find x.
5x+2x=84
7x=84
x=12
m<QRP=60o m<PRS=24o
Types of AnglesTypes of Angles• Acute angle –
• Right angle –
• Obtuse angle –
• Straight angle –
Measures between 0o & 90o
Measures exactly 90o
Measures between 90o & 180o
Measures exactly 180o
Example 5:
• Name an acute angle
<3, <2, <SBT, or <TBC• Name an obtuse angle
<ABT• Name a right angle
<1, <ABS, or <SBC• Name a straight angle
<ABC
12
3
A B C
S
T