如图所示，AB = DC 且 AC = DB。直线 BD 与直线 AC 相交于点 T。

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Identify the three pairs of equal corresponding sides.

In $\triangle ABC$ and $\triangle DCB$ ,

$AB = DC$ given,

$AC = DB$ given,

$BC = CB$ common side.

2. State the congruence conclusion with the correct test.

Since all three corresponding sides are equal,

$\triangle ABC \cong \triangle DCB$ by SSS.

答案

In $\triangle ABC$ and $\triangle DCB$ ,

$AB = DC$ given,

$AC = DB$ given,

$BC = CB$ common side.

Therefore $\triangle ABC \cong \triangle DCB$ by SSS congruence.

1. Use congruence from part (a) to identify equal corresponding angles and relate them to triangle $TBC$.

From part (a), $\triangle ABC \cong \triangle DCB$ .

Therefore corresponding angles are equal:

$\angle ACB = \angle DBC$ .

Since $T$ lies on $AC$ and $DB$ ,

$\angle TCB = \angle TBC$ .

Hence $TB = TC$ , so $\triangle TBC$ is isosceles.

答案

Since $\triangle ABC \cong \triangle DCB$ , corresponding angles are equal.

So $\angle ACB = \angle DBC$ .

Since $T$ lies on $AC$ and $DB$ , $\angle TCB = \angle TBC$ .

Hence $TB = TC$ , so $\triangle TBC$ is isosceles.

AI 分析，可能出错

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