Lesson 10-4: Inscribed Lesson 10-4: Inscribed AnglesAngles

Geometry CPGeometry CP

Mrs. MongoldMrs. Mongold

--Inscribed angleInscribed angle: an angle inside the circle : an angle inside the circle with sides that are chords and a vertex on with sides that are chords and a vertex on the edge of the circlethe edge of the circle Inscribed angle = ½ intercepted arcInscribed angle = ½ intercepted arc

-An inscribed right angle, always intercepts -An inscribed right angle, always intercepts a semicirclea semicircle

-If two or more inscribed angles intercept the -If two or more inscribed angles intercept the same arc, they are congruentsame arc, they are congruent

A

CE

X

Ex: Angle CAE = ½ arc CE

B

A

C

Inscribed angle BAC intercepts a semicircle- so angle BAC =90

D

EF

G

Inscribed angles GDF and GEF both intercept arc GF, so the angles are congruent

Find the measure of angle XFind the measure of angle X

Find the measures of angles 1, 2, Find the measures of angles 1, 2, 3, and 43, and 4

Find the measure of angle RFind the measure of angle R

Find the measure of angle IFind the measure of angle I

Find the measure of angle BFind the measure of angle B

Find the measure of angle DFind the measure of angle D

Find angle S and TFind angle S and T