WELCOME! I see it's that time again where we follow the white rabbit, jump into the hole, and land in GeometryLand once again!
UNIT 8- Christina Cui
-Theorem: The two segments formed from the points of tangency to the intersection of any two tangent lines on the same circle are congruent.
-Theorem: A radius that touches a point of tangency of a tangent line is perpendicular to the tangent line.
-Arc addition postulate: Two adjacent arcs form a larger arc. The measure of the larger arc is the sum of the adjacent arcs.
-Theorem: If a quadrilateral has all 4 points on the circumference of a circle, then the sum of the opposite angles of the quadrilateral is 180.
-Central angle theorem: The measure of an inscribed angle is half the measure of the arc it intercepts.
-Thales' theorem: An inscribed right angle subtends a semi circle.
-Theorem: This theorem states that if a tangent and a secant/chord intersect on a circle at the point of tangency, then the measure of the angle that is made is half the measure of the arc that it touches.
-Theorem: This theorem sates that if two secants or chords intersect in the inside of a circle, then the measure of each angle made is half the sum of the measures of the arcs that it touches.
-Theorem: This theorem states that if a tangent and a secant, two tangents, or two secants intersect on the outside of a circle, then the measure of the angle made is half the difference of the measures of the arcs that it touches.
-Chord-Chord Product Theorem: This theorem states that if two chords intersect on the inside of a circle, then the products of the lengths of the chords' segments are congruent.
-Secant-Secant Product Theorem: This theorem states that if two secants intersect on the outside of a circle, then the product of the lengths of one secant segment and its outer segment equals the product of the lengths of the other secant segment and its outer segment.
-Secant-Tangent Product Theorem: This theorem states that if a secant and a tangent intersect on the outside of a circle, then the product of the lengths of the secant segment and its outer segment equals the length of the tangent segment squared(^2).
I chose these theorems because, of a circle, a variety of different relationships between arc measures, line segments, and angles can be identified and used to better understand a circle's dimensions. The theorems in this unit describe these relationships in formulas that can be used to find missing angles and measures of arcs and segments with the given information.