11.2 Arcs and Chords

Geometry

Definitions:

Central Angle: an angle whose vertex is the center of a circle

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…

Minor arcs may be named by two points. Major arcs and semicircles must be named by three points.

Writing Math

Definitions:

Adjacent Arcs- arcs of the same circle that intersect at exactly one point.

RS and ST are adjacent arcs.

Arc Addition Postulate

Examples:

The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.

Example:

Use the graph to find each of the following. mFMC

mAHB

The circle graph shows the types of cuisine available in a city. Find mTRQ.

Examples:

Find mBD.

Examples:

Find each measure. mJKL

mLJN

Definition:

Congurent Arcs: two arcs that have the same measure.

UVST

Theorems:

Examples:

TV WS. Find mWS.

Example:

Find each measure. mNGH

HL

Theorems:

Example:

A B, and CD EF. Find mCD.

Example:

C J, and mGCD mNJM. Find NM.

Example:

PT bisects RPS. Find RT.

Examples:

Find NP.

Example:

Find QR to the nearest tenth.

Example:

T U, and AC = 47.2. Find PL to the nearest tenth.