More Angle-Arc TheoremsLesson 10.6

Congruent Inscribed & Tangent-Chord Angles

Theorem 89: If two inscribed or tangent-chord angles intercept the same arc, then they are congruent.

Theorem 90: If two inscribed or tangent-chord angles intercept congruent arcs, then they are congruent.

Congruent Inscribed & Tangent-Chord Angles

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.

Special Theorem about Tangent-Tangent Angles

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

1. A is inscribed in a semicircle, it is a right angle.

2. Use the Pythagorean Theorem to solve.

1. (AB)2 + (AC)2 = (BC)2

2. (AB)2 + 402 = 412

3. AB = 9 mm

1. Circle O2. V S

3. L N4. ΔLVE ~ ΔNSE5. EV = EL

SE EN6. EV • EN = EL • SE

1. Given2. If two inscribed s intercept

the same arc, they are .3. Same as 24. AA (2, 3)5. Ratios of corresponding

sides of ~ triangles are =.6. Means-Extremes Products

Theorem.