点D,E在△abc的边bc上,AD=AE,∠BAD=∠CAE,求证:AB=AC

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点D,E在△abc的边bc上,AD=AE,∠BAD=∠CAE,求证:AB=AC

点D,E在△abc的边bc上,AD=AE,∠BAD=∠CAE,求证:AB=AC
点D,E在△abc的边bc上,AD=AE,∠BAD=∠CAE,求证:AB=AC

点D,E在△abc的边bc上,AD=AE,∠BAD=∠CAE,求证:AB=AC
证明:
∵AD=AE
∴∠ADE=∠AED
∵∠ADE=∠BAD+∠B
∠AED=∠CAE+∠C
∠BAD=∠CAE
∴∠B=∠C
∴AB=AC

因为AD=AE,所以∠ADE=∠AED
所以∠ADB=∠AEC
而AD=AE
∠BAD=∠CAE
所以三角形ABD与三角形ACE全等
因此AB=AC