10.4 Use Inscribed Angles and Polygons

Inscribed Angles = ½ the Measure of the Intercepted Arc 90 ̊ 45 ̊

2 Inscribed Angles Corollary If 2 inscribed angles intercept the same arc, then the angles are congruent.If 2 inscribed angles intercept the same arc, then the angles are congruent ̊  1 = m  2 = 55 ̊ m  1 = m  2 = 55 ̊

Inscribed Angle/Semicircle Corollary An angle inscribed in a semicircle is a right angle.An angle inscribed in a semicircle is a right angle.

Inscribe/CircumscribedInscribe/Circumscribed - A circle is circumscribed about a polygon and a polygon is inscribed in a circle when each vertex of the polygon lies on the circle. and a polygon is inscribed in a circle when each vertex of the polygon lies on the circle.

Inscribed Quadrilateral Corollary If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary  1 + m  3 = 180 ̊ m  1 + m  3 = 180 ̊  2 + m  4 = 180 ̊ m  2 + m  4 = 180 ̊

Chord/Tangent Theorem Chord/Tangent Theorem If a tangent and a chord intersect at a point on a circle, then the measure of each  formed is ½ the measure of its intercepted arc. m  1 = ½ m AB m  2 = ½ m BCA ( (

example: Find m  1 = m BCA = m BCA = m  2 = m  2 = 75 o 105 o 210 o