More Angle-Arc Theorems

1. More Angle-Arc Theorems Lesson 10.6

2. Congruent Inscribed & Tangent-Chord Angles Theorem 89: If two inscribed or tangent-chord angles intercept the same arc, then they are congruent.

3. Congruent Inscribed & Tangent-Chord Angles Theorem 90: If two inscribed or tangent-chord angles intercept congruent arcs, then they are congruent.

4. Angles Inscribed in Semi-Circles Theorem 91: An angle inscribed in a semicircle is a right angle. Since the measure of an inscribed angle is one-half the measure of its intercepted arc, and a semi-circle is 180º, C is 90º.

5. Special Theorem about Tangent-Tangent Angles Theorem 92: The sum of the measures of a tangent-tangent angle and its minor arc is 180º.

6. A is inscribed in a semicircle, it is a right angle. • Use the Pythagorean Theorem to solve. • (AB)2 + (AC)2 = (BC)2 • (AB)2 + 402 = 412 • AB = 9 mm

7. Circle O • V  S • L  N • ΔLVE ~ ΔNSE • EV = ELSE EN • EV • EN = EL • SE Given If two inscribed s intercept the same arc, they are . Same as 2 AA (2, 3) Ratios of corresponding sides of ~ triangles are =. Means-Extremes Products Theorem.