Đáp án:

1) $\triangle ABI=\triangle AEI$

2) $AI\bot BE$

3) $\widehat{AEM}=90^o$

Giải thích các bước giải:

1)

Xét $\triangle ABI$ và $\triangle AEI$:

$AB=AE$ (gt)

$AI$: chung

$IB=IE$ (gt)

$\to\triangle ABI=\triangle AEI$ (c.c.c)

$\to\widehat{BAI}=\widehat{EAI}$ (2 góc tương ứng)

2)

$\triangle ABI=\triangle AEI$ (cmt)

$\to\widehat{AIB}=\widehat{AIE}$ (2 góc tương ứng)

Mà $\widehat{AIB}+\widehat{AIE}=180^o$ (kề bù)

$\to\widehat{AIB}=\widehat{AIE}=\dfrac{180^o}{2}=90^o\\\to AI\bot BE$

3)

Xét $\triangle ABM$ và $\triangle AEM$:

$AB=AE$ (gt)

$\widehat{BAM}=\widehat{EAM}\,\,\,(\widehat{BAI}=\widehat{EAI})$

$AM$: chung

$\to\triangle ABM=\triangle AEM$ (c.g.c)

$\to\widehat{ABM}=\widehat{AEM}$ (2 góc tương ứng)

Mà $\widehat{ABM}=90^o\,\,\,(BA\bot BC)$

$\to\widehat{AEM}=90^o$