1.Given that triangle ABC is congruent to triangle EDF,prove that triangle DBG is isosceles.Use any format of proof that you prefer.(下面附图)2.Sylvia has 14 coins,all nickels and quarters.If the value of the coins is $2.90,how many of each type

Question

1.Given that triangle ABC is congruent to triangle EDF,prove that triangle DBG is isosceles.Use any format of proof that you prefer.(下面附图)
2.Sylvia has 14 coins,all nickels and quarters.If the value of the coins is $2.90,how many of each type of coin does she have?Explain your method.

Answer 1

题面是1.已知三角形ABC和三角形EDF相等,求证三角形DBG是等腰三角形.
2.西尔维娅有14枚硬币,其中全部是5分硬币和两角五分的硬币.如果她花费了2.9元,那么她用去了多少五分和两角五分的硬币.写出你的计算过程.
1.证明：
∵△ABC=△EDF,∴∠ABC=∠EDF.
在△DGB中,∠ABC=∠EDF,则DG=BG
∴△DGB是等腰三角形.
2.设五分硬币的数量为x,那么两角五分硬币的数量为14-x,根据题意得
0.05x+0.25(14-x)=2.90
解得 x=3
14-x=14-3=11
答：五分硬币和两角五分硬币 的数量分别是3枚和11枚.