有幾題數吾識做

1.In the figure,straight lines AB,CD and EF intersect at a point O.
prove that x+y+z=180度
From the figure <AOC is x, <DOF is y, <BOE is z
since <COE is equal to < DOF = y
<AOC + <COE + <BOE = 180度
所以，x+y+z = 180度
2.In the figure ,AOC is straight line. IfAOB=3COD,prove thatBO垂直OD
From the figure <BOC is 45度
所以，<AOB = 180度 - <BOC
= 180度 - 45度
= 135度
3<COD = <AOB
<COD = 1/3 * 135度
= 45度
<BOD = <BOC + <COD
= 45度 + 45度
= 90度
所以，BO 垂直 OD

3.In the figure,ABCD and CEFG are two squares.
a)prove that DE=BG
BC = DC
CG = CE
<BCG + <BCD = <DCG
<BCG + 90度 = <DCG --- (1)
<DCE + <ECG = <DCG
<DCE + 90度 = <DCG --- (2)
Sub (2) into (1),
<BCG + 90度 = <DCE + 90度
<BCG = <DCE
所以，△BCG and △DCG are congruent (SAS)
所以，DE = BG
b)If DCG=165度,find BCG&DCE
<DCG = 165度
<DCG = <BCD + <BCG
= 90度 + <BCG
<BCG = 165度 - 90度
= 75度
<DCE = <BCG = 75度
3)If ADE=60度,show that DCE is isosceles.
<ADE = 60度
<CDE= <ADC - <ADE
= 90度 - 60度
= 30度
<DCE = 75度
<DEC = 180度 - <CDE - <DCE
= 180度 - 30度 - 75度
= 75度 = <DCE
所以，△DCE is isosceles
希望解答到你 ^^