如图,△ABC和△DBC中,角BAC=角BDC=90°,O为BC中点（1）△AOD是等腰三角形吗?为什么?

如图,△ABC和△DBC中,角BAC=角BDC=90°,O为BC中点（1）△AOD是等腰三角形吗?为什么?
如图,△ABC和△DBC中,角BAC=角BDC=90°,O为BC中点（1）△AOD是等腰三角形吗?为什么?

如图,△ABC和△DBC中,角BAC=角BDC=90°,O为BC中点（1）△AOD是等腰三角形吗?为什么?
直角三角形,斜边中线=1/2*斜边
补成平行四边形即可证明.

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我想你的图A，D应该是在BC的同一侧（不然就不能确定△AOD的形状了）
则△AOD是等腰三角形
证明：以BC为直径做圆，因为角BAC=角BDC=90°，所以点A，D都在圆上。
O为BC中点，故O为圆心
故OA=OD(都为半径），所以△AOD是等腰三角形