Angles of Tangency — الرياضيات الصف الثالث الإعدادي لغات

درس «Angles of Tangency» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات من وحدة «Angles and Arcs in the circle». This lesson introduces the concept of the angle of tangency, which is an angle formed by a tangent line and a chord passing through the point of tangency. The main theorem states that the measure of an angle of tangency is half the measure of the intercepted arc. This leads to two key corollaries: 1) the angle of tangency equals the inscribed angle subtended by the same arc, and 2) the angle of tangency is half the central angle subtended by the same arc. The lesson also presents the converse theorem: if a ray forms an angle with a chord equal to the inscribed angle in the...

الدرس ده من وحدة «Angles and Arcs in the circle» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات على منصة دروسات.

الدرس متاح بالاشتراك: ترم كامل أو المادة لوحدها.

ملخص الدرس

This lesson introduces the concept of the angle of tangency, which is an angle formed by a tangent line and a chord passing through the point of tangency. The main theorem states that the measure of an angle of tangency is half the measure of the intercepted arc. This leads to two key corollaries: 1) the angle of tangency equals the inscribed angle subtended by the same arc, and 2) the angle of tangency is half the central angle subtended by the same arc. The lesson also presents the converse theorem: if a ray forms an angle with a chord equal to the inscribed angle in the alternate segment, then the ray is tangent to the circle. Applications include proving quadrilaterals are cyclic and proving lines are tangents.

هتتعلم إيه فى الدرس ده

• Definition of an angle of tangency
• Theorem: Angle of tangency is half the measure of the intercepted arc
• Corollary: Angle of tangency equals inscribed angle subtended by the same arc
• Corollary: Angle of tangency is half the central angle subtended by the same arc
• Important note: Angle of tangency is supplementary to the inscribed angle on the other side
• Converse theorem: Ray is tangent if the angle equals the inscribed angle in the alternate segment
• Applications: Proving lines are tangents and proving quadrilaterals are cyclic