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6.3: Arcs and Angles6.4: Proving Circle Conjectures
The Zhaozhou bridge, China, completed in 605 C.E. Theworld’s first stone arched bridge in the shape of a minor arc.
What is an inscribed angle?
Inscribed Angle Conjecture
Inscribed Angle Theorem
360° - 2x -2o = 360°
360° - 360°+ 2x +2o
Theorem:Inscribed Angles intercepting the same arc are congruent.
Since both inscribed ⦟ABC and ⦟ADC intercept the same 𝑨𝑪,then m ⦟ABC = m ⦟ADC
Angles Inscribed in a semicircle:Angles inscribed in a semicircleare right angles.
Cyclic Quadrilateral:Is a quadrilateral inscribed in a circle,all vertices are on the circle.
⦟D + ⦟B = 180° and ⦟A + ⦟C = 180°
𝑨𝑫 ≅ 𝑪𝑩
How are 𝒎 𝑨𝑫 𝒂𝒏𝒅𝒎 𝑪𝑩?
The Angle formed by a Tangent Line and a Secant Line
Examples:1.
2.
3.
Remember
Examples:
Examples:
Homework:Workbook:6.3 & 6.4
Next class: Quiz 6.3
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