12-4 Angle Measures and Segment Lengths
Objectives
To find measures of angles formed by chords, secants, and tangents
To find the lengths of segments associated with circles
Lesson Vocabulary
- secant
Essential Understanding Angles formed by intersecting lines have a special relationship to the related arcs formed when the lines intersect a circle. In this lesson, you will study angles and arcs formed by lines intersecting either within a circle or outside a circle.
Take Note Theorem 12-13
The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs.
Theorem 12-14
The measure of an angle formed by two lines that intersect outside a circle is half the difference of the measures of the intercepted arcs.
You will prove Theorem 12-14 in Exercises 35 and 36.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs