مساله صعبه

[ahmed elbanna]

عندى مساله وعايز حلها
المثلث ا ب ج فيه اد متوسط وقياس زاوية ج>من قياس زاوية ب
اثبت ان قياس زاوية ب ا د>قياس زاوية ج ا د

[طالبه للعلم]

المشاركة الأصلية كتبت بواسطة ahmed elbanna

عندى مساله وعايز حلها
المثلث ا ب ج فيه اد متوسط وقياس زاوية ج>من قياس زاوية ب
اثبت ان قياس زاوية ب ا د>قياس زاوية ج ا د

ممكن رسم توضيحى ؟

[ahmed elbanna]

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[masterahmed2050]

أولا المطلوب أصغر وليس أكبر وهذا هو الحل

[ahmed elbanna]

متشكر جدا جدا وما شاء الله عليك وعلى اسلوبك

[آيه إبراهيم]

عندى حل آخر اتمنى ان يكون صحيح

العمل : نرسم الشعاع (ب أ) ونأخذ عليه النقطه هـ ونصل النقطه جـ بالنقطه هـ
البرهان :
بما ان (أ) منتصف ب هـ بما ان د منتصف ب جـ
اذن أ د يوازى ب هـ
اذن قياس زاويه (ب أ د ) = ق (^هـ) بالتناظر
اذن ق ( ^جـ أ د ) = ق (^أ جـ هـ) بالتبادل
بما ان ق(^أ جـ ب)> ق(ب)
اذن أب >أ جـ
بما ان أب = أ هـ
اذن أهـ >أجـ
اذن ق (^أ جـ هـ)> ق(^هـ)
اذن قياس زاويه (جـ أ د)>ق(^ب أ د)









أتمنى من الله ان يكون الحل صحيح فلقد توصلت اليه بعد تفكير طويل

[masterahmed2050]

المشاركة الأصلية كتبت بواسطة ahmed elbanna

متشكر جدا جدا وما شاء الله عليك وعلى اسلوبك

الشكر لله وحده
أسأل بس واحنا نجاوب باذن الله

[masterahmed2050]

أتمنى من الله ان يكون الحل صحيح فلقد توصلت اليه بعد تفكير طويل

طبعا صحيح وطريقة ممتعة أحسنتى