Inscribed Angles PDF

Inscribed Angles  INSCRIBED ANGLE An inscribed angle in a circle is an angle whose vertex is on the circle and whose sides contain chords of the circle.  Theorem 97: The Inscribed Angle Theorem The measure of an inscribed angle is one-half...

Inscribed Angles  INSCRIBED ANGLE An inscribed angle in a circle is an angle whose vertex is on the circle and whose sides contain chords of the circle.  Theorem 97: The Inscribed Angle Theorem The measure of an inscribed angle is one-half the measure of its intercepted arc. 1 m∠𝐴 = 𝑚 𝐵𝐶 2 𝑚 𝐵𝐶 = 2m∠𝐴  Theorem 98: Semicircle Theorem An angle inscribed in a semicircle is a right angle  Theorem 99: Inscribed Angles in the Same Arc Theorem Two or more angles inscribed in the same arc are congruent Refer to the figure at the right. 1. Name the angles that are intercept 𝐴𝑃 Refer to the figure at the right. 2. Name the angles that are intercept 𝐸𝑉 Refer to the figure at the right. 3. Name the arc that intercepted by ∠𝑃𝐴𝐸 Refer to the figure at the right. 4. Name the arc that intercepted by ∠𝐸𝑉𝑃  Theorem 100: Inscribed Quadrilateral Theorem Opposite angles of an inscribed quadrilateral are supplementary. The quadrilateral ABCD is inscribed in a circle E. Find the indicated measure. 𝑚∠𝐴𝐵𝐶 = 85, 𝑚∠𝐴𝐷𝐶 = The quadrilateral ABCD is inscribed in a circle E. Find the indicated measure. m𝐴𝐷 = 110, 𝑚∠𝐴𝐸𝐷 = The quadrilateral ABCD is inscribed in a circle E. Find the indicated measure. m∠𝐷𝐴𝐵 = 93, 𝑚 𝐵𝐶𝐷 = The quadrilateral ABCD is inscribed in a circle E. Find the indicated measure. m𝐷𝐴𝐵 = 190, 𝑚∠𝐵𝐶𝐷 = The quadrilateral ABCD is inscribed in a circle E. Find the indicated measure. m𝐴𝐷 = 105, m 𝐴𝐵 = 75, 𝑚∠𝐷𝐶𝐵 =  A Find the measures of the 90° following 14 1. m∠1 2. m∠2 E F G 3. m∠3 5 4. m∠4 2 5. m∠5 3 B 6. m∠𝐴𝐹𝐺 D 7. m∠𝐷𝐴𝐵 45° C 45°