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第二十八章　圓
28. 3 圓心角和圓周角
第1課時　圓心角及其性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．找出圖中所有的弦、優弧和劣弧．
INCLUDEPICTURE"冊93.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊93.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊93.tif" \* MERGEFORMATINET
INCLUDEPICTURE"預習效果檢測.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET
1．頂點在________的角叫做圓心角．
2．在同圓或等圓中，相等的圓心角所對的弦________，所對的弧__________．
3．在同圓或等圓中，兩個圓心角及其所對應的兩條弦和所對應的兩條弧這三組量中，只要有一組量________，其他兩組量就分別________．
4．在同圓或等圓中，若的長度等于的長度，則下列說法正確的有(　　)
①所對的圓心角等于所對的圓心角；②和是等弧；
③所對的弦長等于所對的弦長．
A．0個 B．1個 C．2個 D．3個
5．[2023麗水期中]如圖，若∠AOB＝40°，則所對的圓心角的度數是________．
INCLUDEPICTURE"冊94.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊94.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊94.tif" \* MERGEFORMATINET
6．如圖，A，B，C，D是⊙O上的點，已知∠AOB＝∠COD，求證：AC＝BD.
INCLUDEPICTURE"冊95.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊95.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊95.tif" \* MERGEFORMATINET
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識點1 圓心角的概念
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 下面圖形中的角是圓心角的是(　　)
　　　　　　　　　　　　
變式1下列說法正確的是(　　)
A．如果一個角的一邊過圓心，則這個角就是圓心角
B．圓心角α的取值范圍是0°＜α＜180°
C．圓心角就是頂點在圓心，且角的兩邊是兩半徑所在的射線的角
D．圓心角就是頂點在圓內的角
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知識點2 弧、 弦、圓心角之間的關系
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023邢臺期末]如圖，AB是⊙O的直徑，＝，∠COD＝50°，求∠AOD的度數．
INCLUDEPICTURE"冊100.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊100.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊100.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
變式2－1已知弦AB把圓周分成1∶3兩部分，則劣弧AB所對圓心角的度數為(　　)
A．90° B．270° C．45° D．135°
變式2－2如圖，A，B，C，D是⊙O上的點，如果AB＝CD，∠AOB＝70°，那么∠COD＝________．
INCLUDEPICTURE"冊101.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊101.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊101.tif" \* MERGEFORMATINET
第2課時　圓周角及其性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．圓心角指頂點在________的角．
2．如圖，AB，CD是⊙O的兩條弦：
INCLUDEPICTURE"冊102.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊102.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊102.tif" \* MERGEFORMATINET
①如果AB＝CD，那么____________，____________；
②如果＝，那么____________，____________；
③如果∠AOB＝∠COD，那么____________，____________．
INCLUDEPICTURE"預習效果檢測.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET
1．頂點在________，兩邊都與圓________的角叫做圓周角．
2．圓周角定理：圓上一條弧所對的圓周角等于它所對的________的一半．
3．半圓(或直徑)所對的圓周角是________，90°的圓周角所對的弦是________．
4．如圖，所對的圓周角是__________，所對的圓周角是__________．
INCLUDEPICTURE"冊103.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊103.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊103.tif" \* MERGEFORMATINET (第4題)　　INCLUDEPICTURE"冊104.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊104.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊104.tif" \* MERGEFORMATINET (第5題)　　
5．[2023無錫期中]如圖，A，B，C三點在⊙O上，且∠A＝50°，則∠BOC的度數為(　　)
A．100° B．120° C．130° D．150°
6．[2023杭州期中]如圖，AB是⊙O的直徑，點C在圓上，若所對的圓心角為64°，則∠CBA的度數為(　　)
(第6題)
A．32° B．64° C．68° D．58°
7．如圖，點A，B，C在⊙O上，∠ACB＝50°，求∠OAB的度數．
INCLUDEPICTURE"小冊1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\小冊1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\小冊1.tif" \* MERGEFORMATINET
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識點1 圓周角
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET [2023唐山期末]下列圖形中，∠BAC是圓周角的是(　　)
變式1如圖，△ABC內接于⊙O，弦BD交AC于點P，連接AD.下列角中，是所對的圓周角的是(　　)
INCLUDEPICTURE"冊110.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊110.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊110.tif" \* MERGEFORMATINET
A．∠APB B．∠ABD C．∠ACB D．∠BAC
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知識點2 圓周角定理
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023邢臺期末]如圖，在⊙O中，∠AOB＝130°，則∠C的度數為________．
INCLUDEPICTURE"冊111.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊111.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊111.tif" \* MERGEFORMATINET
變式2如圖，在⊙O中，∠OBA＝34°，點D是上的一點，則∠ADB的度數為(　　)
INCLUDEPICTURE"冊112.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊112.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊112.tif" \* MERGEFORMATINET
A．54° 　 B．56° C．58° D．60°
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知識點3 圓周角定理的推論
INCLUDEPICTURE"L3.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L3.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L3.tif" \* MERGEFORMATINET 如圖，在△ABC中，AB＝AC，∠C＝70°，以AB為直徑的⊙O交BC于點D，則所對圓心角的度數為________°.
INCLUDEPICTURE"冊113.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊113.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊113.tif" \* MERGEFORMATINET
變式3[2023周口期末]將一個含60°角的直角三角板和一個量角器按如圖所示的方式放置，∠ACB＝90°，其中點D所在位置在量角器外側的讀數為30°，連接DC交AB于點E，則圖中∠BEC的度數是(　　)
INCLUDEPICTURE"冊114.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊114.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊114.tif" \* MERGEFORMATINET
A．75° 　 B．65° C．55° D．45°
第3課時　圓內接四邊形及其性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．如圖，點O是△ABC的外接圓的圓心，若∠A＝80°，則∠BOC的度數為(　　)
A．100° B．160° C．150° D．130°
INCLUDEPICTURE"冊115.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊115.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊115.tif" \* MERGEFORMATINET (第1題)　　　INCLUDEPICTURE"冊116.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊116.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊116.tif" \* MERGEFORMATINET (第2題)
2．如圖，在四邊形ABCD中，∠B與∠1互補，AD的延長線與DC所夾的∠2＝60°，則∠1＝________，∠B＝________．
INCLUDEPICTURE"預習效果檢測.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET
1．________所對的圓周角相等．
2．四個頂點都在同一個圓上的四邊形叫做____________，這個圓叫做四邊形的________．
3．圓內接四邊形的對角________．
4．[2023北京西城區期中]如圖，A，B，C三點在已知的圓上，在△ABC中，∠ABC＝70°，∠ACB＝30°，D是上的一點，分別連接DB，DC，則∠D的度數為(　　)
A．30° B．80° C．90° D．70°
INCLUDEPICTURE"冊117.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊117.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊117.tif" \* MERGEFORMATINET (第4題)　　　　　INCLUDEPICTURE"冊118.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊118.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊118.tif" \* MERGEFORMATINET (第5題)
5．[2023北京西城區期中]如圖，點A，B，C，D在⊙O上，∠DAB＝40°，則∠DCB的度數為(　　)
A．80° B．100° C．140° D．160°
6．在圓內接四邊形ABCD中，∠A，∠B，∠C的度數的比是3∶2∶7，求四邊形各內角的度數．
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識點1 同弧所對的圓周角相等
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 如圖，AB是⊙O的直徑，∠BCD＝50°，則∠ABD的度數是(　　)
INCLUDEPICTURE"冊119.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊119.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊119.tif" \* MERGEFORMATINET
A．50° B．40° C．30° D．25°
變式1[2023許昌期末]如圖，在⊙O中，弦AB，CD相交于點P，若∠A＝50°，∠APD＝82°，則∠B的大小是(　　)
INCLUDEPICTURE"冊120.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊120.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊120.tif" \* MERGEFORMATINET
A．32° B．42° C．48° D．52°
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知識點2　圓內接四邊形
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023南京期中]如圖，在△ABC中，AB＝AC，過點A，C的⊙O與BC，AB分別交于點D，E，連接DE.
(1)求證：DB＝DE；
(2)延長ED，AC相交于點P，若∠P＝33°，則∠A的度數為________°.
INCLUDEPICTURE"冊121.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊121.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊121.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　　
變式2－1[2023南昌期末]如圖，點A，B，C都在⊙O上，∠C＝100°，則∠O＝(　　)
INCLUDEPICTURE"冊122.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊122.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊122.tif" \* MERGEFORMATINET
A．110° B．120° C．150° D．160°
變式2－2已知在四邊形ABCD中，∠B＝90°，AB＝3，BC＝4，CD＝，AD＝2，試判斷A，B，C，D四點是否在同一個圓上，并說明理由．
INCLUDEPICTURE"冊123.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊123.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊123.tif" \* MERGEFORMATINET
28. 3 圓心角和圓周角
第1課時　圓心角及其性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．解：弦：弦AB，弦CD，弦AD；
優弧：，，，；
劣弧：，，，.
INCLUDEPICTURE"預習效果.tif" INCLUDEPICTURE "預習效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET
1．圓心　2.相等；也相等　3.相等；相等　4.D　5.40°
6．證明：∵∠AOB＝∠COD，
∴∠AOB＋∠BOC＝∠COD＋∠BOC，
即∠AOC＝∠BOD，∴AC＝BD.
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "課堂導學.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
例1　D　變式1.C
例2　解：∵在⊙O中，AB是⊙O的直徑，∴∠AOB＝180°.
∵＝，∴∠BOC＝∠COD＝50°，
∴∠AOD＝180°－50°－50°＝80°.
變式2－1.A　變式2－2.70°
第二十八章　圓
28. 3 圓心角和圓周角
第2課時　圓周角及其性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．圓心
2．①＝；∠AOB＝∠COD
②AB＝CD；∠AOB＝∠COD
③AB＝CD；＝
INCLUDEPICTURE"預習效果.tif" INCLUDEPICTURE "預習效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET
1．圓上；相交　2.圓心角　3.直角；直徑
4．∠BDC；∠CBD，∠CAD　5.A　6.D
7．解：連接OB，∵∠ACB＝50°，
∴∠AOB＝2∠ACB＝100°.
∵OA，OB都是⊙O的半徑，∴OA＝OB.
∴∠OAB＝∠OBA＝＝40°.
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "課堂導學.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
例1　B　變式1.C　例2　65°　變式2.B
例3　40　變式3.D
第3課時　圓內接四邊形及其性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．B　2.120°；60°
INCLUDEPICTURE"預習效果.tif" INCLUDEPICTURE "預習效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET
1．同弧　2.圓內接四邊形；外接圓　3.互補　4.B　5.C
6．解：∵∠A，∠B，∠C的度數的比是3∶2∶7，
∴設∠A，∠B，∠C的度數分別為3x，2x，7x.
∵四邊形ABCD是圓內接四邊形，
∴∠A＋∠C＝180°，∠B＋∠D＝180°，
∴3x＋7x＝180°，∴x＝18°，
∴∠A＝3x＝54°，∠B＝2x＝36°，∠C＝7x＝126°.
又∵∠B＋∠D＝180°，
∴∠D＝180°－∠B＝180°－36°＝144°.
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "課堂導學.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
例1　B　變式1.A
例2　(1)證明：∵AB＝AC，∴∠B＝∠C.
∵四邊形AEDC為⊙O的內接四邊形，
∴∠AED＋∠C＝180°，
又∵∠AED＋∠BED＝180°，
∴∠BED＝∠C，
∴∠BED＝∠B，∴DB＝DE.
(2)38
變式2－1.D　
變式2－2.解：連接AC，
∵在△ABC中，∠B＝90°，AB＝3，BC＝4，
∴AC＝＝＝5.
∵在△ADC中，AD2＋DC2＝22＋()2＝52＝AC2，
∴∠D＝90°，∴∠B＋∠D＝180°.
又∵∠B＋∠BCD＋∠D＋∠BAD＝360°，
∴∠BCD＋∠BAD＝180°，
∴A，B，C，D四點在同一個圓上．

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