如图所示,在ΔABC中,∠C=90º,AD平分∠CAB,与∠ABC的平分线BE相交于点D,求∠ADE的度数.
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![如图所示,在ΔABC中,∠C=90º,AD平分∠CAB,与∠ABC的平分线BE相交于点D,求∠ADE的度数.](/uploads/image/z/14447522-2-2.jpg?t=%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA%2C%E5%9C%A8%CE%94ABC%E4%B8%AD%2C%E2%88%A0C%EF%BC%9D90%26%23186%3B%2CAD%E5%B9%B3%E5%88%86%E2%88%A0CAB%2C%E4%B8%8E%E2%88%A0ABC%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BFBE%E7%9B%B8%E4%BA%A4%E4%BA%8E%E7%82%B9D%2C%E6%B1%82%E2%88%A0ADE%E7%9A%84%E5%BA%A6%E6%95%B0.)
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如图所示,在ΔABC中,∠C=90º,AD平分∠CAB,与∠ABC的平分线BE相交于点D,求∠ADE的度数.
如图所示,在ΔABC中,∠C=90º,AD平分∠CAB,与∠ABC的平分线BE相交于点D,求∠ADE的度数.
如图所示,在ΔABC中,∠C=90º,AD平分∠CAB,与∠ABC的平分线BE相交于点D,求∠ADE的度数.
∵AD、BD分别平分∠CAB、∠CBA,
∴∠DAB=1/2∠CAB,∠DBA=1/2∠CBA,
∴∠ADE=∠DAB+∠DBA (三角形的外角等于与它不相邻的两个内位角和)
=1/2(∠CAB+∠CBA)
=1/2(180°-∠C)
=45°.
∠ADE=∠DAB+∠DBA=1/2∠CAB+1/2∠CBA=1/2*90=45度