Lesson 10.6.  Theorem 89: If two inscribed or tangent- chord angles intercept the same arc, then they are congruent.

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Presentation transcript:

Lesson 10.6

 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.

 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 180 º,  C is 90 º.

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

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) = AB = 9 mm

1.Circle O 2.  V   S 3.  L   N 4.Δ LVE ~ Δ NSE 5.EV = EL SE EN 6.EV EN = EL SE 1.Given 2.If two inscribed  s intercept the same arc, they are . 3.Same as 2 4.AA (2, 3) 5.Ratios of corresponding sides of ~ triangles are =. 6.Means-Extremes Products Theorem.