Proofs That Involve Chords, Angles, and Arcs. Part 1

This is a collection of proofs that has chords forming inscribed angles, intersecting congruent arcs, or intersecting to bisect angles, or to form similar triangles. Proofs show a step by step solution that highlights all features in the associated figure, as the proof is built.

Lesson's Content

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.

Radii
Plural form of radius

Radius
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.

This figure has an inscribed angle and a central angle intersecting the same arc in the

circle. Try Dragging any of the points "A" or "B" in the figure to check the existing relationship:

The central angle is twice the measure of the inscribed angle intersecting the same arc.

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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