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