Day 1

Tangent Chord VOCAB Inscribed Angle Central Angle Secant

Chord: A segment with endpoints that are on the circle Tangent: A line that intersects the circle in exactly one point (touches, but does not cross through) Inscribed Angle: An angle that has a vertex on a circle and sides that contain chords of the circle Central Angle: An angle that intersects a circle in two points and has its vertex at the center of the circle Secant: Any line that intersects a circle in exactly two points

Major Arc Minor Arc A Minor Arc = 𝐴𝐵 Major Arc = 𝐴𝐶𝐵 Named by two endpoints Measures between 0°<𝜃<180° Named by Three points (two endpoints with one in between) Measures 𝜃>180° Major Arc B E C Semicircle = 𝐵𝐷𝐶 Circle = ⊙E Named by its “Center” “Circle E” Measures exactly 𝜃=360° Named by Three points (two endpoints with one in between) Measures exactly 𝜃=180° D

Inscribed Quadrilateral Inscribed Quadrilateral: F F 𝑬𝑿 𝟏: VOCAB: <𝐶𝐹𝐷 is an INSCRIBED ANGLE <𝑪𝑭𝑫= 𝟏 𝟐 𝒎 𝑪𝑫 Inscribed Quadrilateral A B C D B C E 𝑉𝑂𝐶𝐴𝐵: <𝐶𝐸𝐷 is a CENTRAL ANGLE <𝑪𝑬𝑫=𝒎 𝑫𝑪 𝑬𝑿 𝟐: Inscribed Quadrilateral: Opposite Angles are SUPPLEMENTARY! Central Angle D

𝐄𝐗 𝟏: 𝟗𝟎°= 𝒎 𝑪𝑫 If <𝑪𝑭𝑫=𝟒𝟓°, 𝒇𝒊𝒏𝒅 𝒎 𝑪𝑫 <𝑪𝑭𝑫= 𝟏 𝟐 𝒎 𝑪𝑫 C D F If <𝑪𝑭𝑫=𝟒𝟓°, 𝒇𝒊𝒏𝒅 𝒎 𝑪𝑫 𝟒𝟓° <𝑪𝑭𝑫= 𝟏 𝟐 𝒎 𝑪𝑫 𝟒𝟓= 𝟏 𝟐 𝒎 𝑪𝑫 𝟗𝟎°= 𝒎 𝑪𝑫

EX 2: If Opposite angles are supplementary in an inscribed quadrilateral, find the following measure. <𝐷=71° Find the measure of <𝐵 A B C D <D+<B=180 71+<B=180 <B=109°