Download More Angle-Arc Theorems

Lesson 10.6
 Theorem
89: If two inscribed or tangentchord angles intercept the same arc, then
they are congruent.
 Theorem
90: If two inscribed or tangentchord 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 180º, C is 90º.
 Theorem
92: The sum of the measures of
a tangent-tangent angle and its minor arc
is 180º.
1.
2.
A is inscribed in a semicircle, it is a
right angle.
Use the Pythagorean Theorem to solve.
1. (AB)2 + (AC)2 = (BC)2
2.
3.
(AB)2 + 402 = 412
AB = 9 mm
1. Circle O
2. V  S
3. L  N
4. ΔLVE ~ ΔNSE
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.