Inscribed Angles Subtended by the Same Arc — الرياضيات الصف الثالث الإعدادي لغات

درس «Inscribed 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 theorem that all inscribed angles subtended by the same arc are equal in measure. The proof is straightforward: since each inscribed angle is half the measure of the intercepted arc, they are all equal to the same value. The lesson also proves the converse corollary: inscribed angles of equal measure subtend arcs of equal measure. Several applications are presented: proving equal segments when chords intersect, proving angles are equal when chords are equal, and determining whether four points are concyclic (lie on the same...

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 theorem that all inscribed angles subtended by the same arc are equal in measure. The proof is straightforward: since each inscribed angle is half the measure of the intercepted arc, they are all equal to the same value. The lesson also proves the converse corollary: inscribed angles of equal measure subtend arcs of equal measure. Several applications are presented: proving equal segments when chords intersect, proving angles are equal when chords are equal, and determining whether four points are concyclic (lie on the same circle) based on equal angles subtended by the same base segment.

هتتعلم إيه فى الدرس ده

• Theorem: Inscribed angles subtended by the same arc are equal
• Proof of the theorem using the arc measure
• Converse corollary: equal inscribed angles subtend equal arcs
• Application: Proving equal segments when two chords intersect
• Application: Proving angles are equal using equal chords
• Condition for four points to be concyclic (equal angles on the same base)
• Problem solving involving intersecting circles