math question

[jo jo]

见附件

 

[dkwan]

共綫怎麼証明？

 

[哈哈哈镜]

180

 

[jo jo]

怎么证明180

 

[9981]

First, ABC and ADC are two Equilateral triangle.
<AMP = 60
<PAD = 60
Then
<CPA+<DAQ = 60
Because
<DAQ+ <CAQ = <DAC = 60
THEN
<CAQ = < CPA
----------------------------------------------
Because
<CAP = <ACQ = 120
ACP and ACQ are Similarity triangle.
Then
AP/AC = AC/QC
-----------------------------------------------
because
AC = AD = DC
AP/AC = AP/AD
AC/QC = DC/QC
THEN
AP/AD = DC/QC
<PAD = <DCQ = 60
PAD and DCQ are Similarity triangle.
------------------------------------------------
THEN
<PDA = <DQC
THEN <PDA+ <ADC+ <CDQ = <DQC+ 60 +CDQ = 180

 

[jo jo]

thank you, Mathematician