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

You have worked by now problems with similarity applied to triangles, and figures with triangles embedded in those composite figures. In this section you will do the same but inside circles, and with theorems that relate inscribed angles that are part of those triangles and the chords that they intersect, or the same with angles centered at the circle, known as central angles. You will build the proof in a step by step mode following the sequence of animations and colors to guide the logic process. If you try the suggested problems; you will be able to solve them with your stylus and taking advantage of the marker tools menu.

Lesson's Content

Lesson In PDF Format (no animations)

PURCHASE INFORMATION

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.

 

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