题目内容

As shown in figure point C is on the segment BG and quadrilateral ABCD is a square．AG intersects BD and CD at points E and F，respectively．If AE=5 and EF=3，then FG=
（英汉词典：square正方形．intersect…at…与…相交于…）

A.
$数学公式$
B.
$数学公式$
C.
4
D.
5

A
分析：由AD∥BC可得 $\text{[math]}$ = $\text{[math]}$ ，由AB∥CD，AD=BC可得 $\text{[math]}$ = $\text{[math]}$ = $\text{[math]}$ ，进而即可求解FG的值．
解答：在正方形ABCD中，则AD∥BC，AB∥CD，AD=BC，
∴ $\text{[math]}$ = $\text{[math]}$ = $\text{[math]}$ ，
又AD=BC，在△ABG中，
∴ $\text{[math]}$ = $\text{[math]}$ = $\text{[math]}$ = $\text{[math]}$ ，
即 $\text{[math]}$ = $\text{[math]}$ ，
解得FG= $\text{[math]}$ ．
故选A．
点评：本题主要考查了正方形的性质以及相似三角形的判定及性质问题，能够熟练掌握．

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As shown in figure point C is on the segment BG and quadrilateral ABCD is a square．AG intersects BD and CD at points E and F，respectively．If AE=5 and EF=3，then FG=（英汉词典：square正方形．intersect…at…与…相交于…）

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As shown in figure point C is on the segment BG and quadrilateral ABCD is a square．AG intersects BD and CD at points E and F，respectively．If AE=5 and EF=3，then FG=
（英汉词典：square正方形．intersect…at…与…相交于…）