inscribed angles. inscribed angles and central angles a central angle has a vertex that lies in the...
TRANSCRIPT
Inscribed Angles
Inscribed Angles and Central Angles
A Central angle has a vertex that lies in the center of a circle.
An inscribed angle hasa vertex that lies on the edge of a circleand its two sides are chords of the circle.
Measurements of Central Angles
The measure of a central angle is equal to the measure of its intercepted arc.
x°
80
280
Therefore the measure of angle X must be 80°.
Measurements of Inscribed AnglesThe measure of an inscribed angle is
equal to the half the measure of its intercepted arc.
80
280
Therefore the measure of angle X must be 40°. x°
Identifying Intercepted Arcs
1
Identify the Intercepted Arc
for 1The intercepted
Arc for
1 AD
1
Identifying Intercepted Arcs
2
Identify the Intercepted Arc
for 2The intercepted
Arc for
2 BC 22
Identifying Intercepted Arcs
3
Identify the Intercepted Arc
for 3The intercepted
Arc for
3 BC
3
Making Conjectures
3
Make a conjecture about
2& 3 2
They are congruent
because they share the same intercepted arc.
Identifying Intercepted Arcs
Identify the Intercepted Arc
for BCDThe intercepted
Arc for
BCD BAD
Identifying Intercepted Arcs
Identify the Intercepted Arc
for ABCThe intercepted
Arc for
ABC ADC
Determining Measures of Inscribed Angles
Determine the measure
of EDA
The measure of EDA 30
Determining Measures of Inscribed Angles
Determine the measure
of ADB
The measure of ADB 47.5
Determining Measures of Inscribed Angles
Determine the measure
of BAD
The measure of BAD 67.5
Determining Measures of Inscribed Angles
Determine the measure
of ABC
The measure of
ABC 90
Determining Measures of Inscribed Angles
Determine the measure
of BDC
The measure of EDA 42.5
Determining Measures of Inscribed Angles
Determine the measure
of CAD
The measure of EDA 25
Determining Measures of Arcs
Determine the measure
of AC
The measure of AC 110
Determining Measures of Arcs
Determine the measure
of DC
The measure of DC 100
Determining Measures of Arcs
Determine the measure
of BC
The measure of BC 40
Determining Measures of Arcs
Determine the measure
of ED
The measure of ED 75
Determining Measures of Arcs
Determine the measure
of EDB
The measure of EDB 215