Cyclic Quadrilaterals — الرياضيات الصف الثالث الإعدادي لغات

درس «Cyclic Quadrilaterals» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات من وحدة «Angles and Arcs in the circle». This lesson introduces the concept of a cyclic quadrilateral: a quadrilateral whose four vertices all lie on the same circle. The lesson provides two criteria for identifying a cyclic quadrilateral: 1) all four vertices lie on a circle, and 2) two angles subtended by the same base and on the same side are equal. The lesson includes two examples: proving that the quadrilateral formed by the midpoints of two sides of a triangle and the circumcenter is cyclic, and proving that a specific quadrilateral formed by points on the diagonals of a cyclic quadrilateral is also cyclic...

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 a cyclic quadrilateral: a quadrilateral whose four vertices all lie on the same circle. The lesson provides two criteria for identifying a cyclic quadrilateral: 1) all four vertices lie on a circle, and 2) two angles subtended by the same base and on the same side are equal. The lesson includes two examples: proving that the quadrilateral formed by the midpoints of two sides of a triangle and the circumcenter is cyclic, and proving that a specific quadrilateral formed by points on the diagonals of a cyclic quadrilateral is also cyclic. The key property used is that if two angles subtend the same base and are equal, the four points are concyclic.

هتتعلم إيه فى الدرس ده

• Definition of a cyclic quadrilateral
• Criterion 1: All four vertices lie on a circle
• Criterion 2: Two angles subtended by the same base are equal
• Example: Proving AXYM is cyclic
• Example: Proving BXYC is cyclic
• Application: Proving other quadrilaterals are cyclic
• Using the cyclic property to prove angle equalities