11 2 Arcs and Chords Geometry Definitions l

11. 2 Arcs and Chords Geometry

Definitions: l Central Angle: an angle whose vertex is the center of a circle l Arc- an unbroken part of a circle consisting of two points called endpoints and all of the points between them

Arcs and Their Measures

Helpful Hints… Writing Math Minor arcs may be named by two points. Major arcs and semicircles must be named by three points.

Definitions: l Adjacent Arcs- arcs of the same circle that intersect at exactly one point. l RS and ST are adjacent arcs.

Arc Addition Postulate

Examples: l The circle graph shows the types of grass planted in the yards of one neighborhood. Find m. KLF.

Example: l Use the graph to find each of the following. l m FMC l m. AHB

l The circle graph shows the types of cuisine available in a city. Find m. TRQ.

Examples: l Find m. BD.

Examples: l Find each measure. l m. JKL l m. LJN

Definition: l Congurent Arcs: two arcs that have the same measure.

Theorems:

Examples: l TV WS. Find m. WS.

Example: l Find each measure. l m. NGH l HL

Theorems:

Example: l A B, and CD EF. Find m. CD.

Example: l C J, and m GCD m NJM. Find NM.

Example: l PT bisects RPS. Find RT.

Examples: l Find NP.

Example: l Find QR to the nearest tenth.

Example: l T U, and AC = 47. 2. Find PL to the nearest tenth.