已知：如图,AD、A‘D‘分别是△ABC和△A’B‘C‘的高,AB=A’B‘,AD=A’D‘,BC=B‘C’求证：AC=A‘C’

Question

已知：如图,AD、A‘D‘分别是△ABC和△A’B‘C‘的高,AB=A’B‘,AD=A’D‘,BC=B‘C’ 求证：AC=A‘C’

Answer 1

∵AB＝A′B′、AD＝A′D′、∠ADB＝∠A′D′B′＝90°,∴△ABD≌△A′B′D′,∴∠B＝∠B′.
由AB＝A′B′、BC＝B′C′、∠B＝∠B′,得：△ABC≌△A′B′C′,∴AC＝A′C′.