The relation between the inscribed and central angles subtended by the same arc — الرياضيات الصف الثالث الإعدادي لغات

درس «The relation between the inscribed and central angles subtended by the same arc» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات من وحدة «Angles and Arcs in the circle». This lesson establishes the fundamental relationship between inscribed angles and central angles. The main theorem states: the measure of an inscribed angle is half the measure of the central angle subtended by the same arc. The lesson proves the theorem for the case where the center lies on one side of the inscribed angle and asks students to prove the other two cases. Corollaries are derived: the measure of an inscribed angle is half the measure of its intercepted arc, and an inscribed angle in a semicircle is a...

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 establishes the fundamental relationship between inscribed angles and central angles. The main theorem states: the measure of an inscribed angle is half the measure of the central angle subtended by the same arc. The lesson proves the theorem for the case where the center lies on one side of the inscribed angle and asks students to prove the other two cases. Corollaries are derived: the measure of an inscribed angle is half the measure of its intercepted arc, and an inscribed angle in a semicircle is a right angle. The lesson also covers two well-known problems: intersecting chords inside a circle (angle = 1/2 (sum of opposite arcs)) and intersecting secants outside a circle (angle = 1/2 (difference of arcs)).

هتتعلم إيه فى الدرس ده

• Definition of an inscribed angle
• Theorem: Inscribed angle is half the central angle subtended by the same arc
• Proof of the theorem (three cases)
• Corollary: Inscribed angle is half the measure of the subtended arc
• Corollary: Inscribed angle in a semicircle is a right angle
• Application problems involving inscribed angles
• Well-known problem 1: Intersecting chords inside a circle
• Well-known problem 2: Intersecting secants outside a circle