# Proofs That Involve Chords, Angles, and Arcs. Part 2

### Working proofs that apply theorems for secants, tangents and chords.

Lesson's Content

 Lesson In PDF Format (no animations)

Lesson's Glossary

Arc
Curved segment in a circle.

Center of a circle
The point that all points in the circle are equidistant from

Central angle of a circle
An angle whose vertex is the center of the circle

Chord of a circle
A segment whose endpoints are on a circle

Circle
The set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides

Postulate
A statement assumed to be true without proof.

Proof
A sequence of justified conclusions used to prove the validity of an if-then statement.

The segment whose endpoints are any point on a circle or sphere and its center; the length of that segment

Semicircle
An arc whose central angle is a right angle

Interactive Geometric Applets: Relevant Theorems.

If you have a diameter perpendicular to the chord, then this cuts in half to

both the chord, and its intercepted arc. This theorem may be verified

by dragging up and down point "B". Pay special attention on how

the chord and the arc update their bisected values.

Two inscribed angles intersecting the congruent arcs in the same circle or in congruent circles

are congruent. You manipulate this interactive applet by dragging the vertices of the

inscribed angles, or the endpoints in the arc. Verify that the angles remain congruent.

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