By alternate angles, angle BDE = angle CBD = x, then by isosceles triangle, BE = DE = AE and so angle BAE = x as well. Then x = 45 degrees. Hence I, II, and III are true. You dont need any extra info...
So long as the order of vertices is ABCD, you can construct the parallelogram in any way you like and you still get the right conclusion despite awkward shapes. The steps: (1) let equal angles be x (2) angle BDE = x (alt angles // lines) (3) triangle BDE isosceles (base angles equal to x) (4) BE = DE (equal sides of isosceles triangle BDE) (5) triangle ABE isoceles triangle (equal sides BE = DE = AE as given) (6) angle BAE = x (base angles of isosceles triangle equal) (7) triangle ADB isosceles triangle (base angles equal to x) (8) AB = BD (equal sides of isoceles triangle ADB) (hence I correct) (9) angle sum of triangle ADB = 4x = 180 and given angle ABC = 3x = 135) (hence II correct) (10) triangle ABE and triangle DBE are congruent (SAS: AB = BD as equal sides of isosceles triangle ADB, common side BE, inclusive angles equal to x as given) (hence III correct). The whole derivation and conclusion are straight forward and independent of the shape drawn. Don't waste time searching for a correct shape. The actual reason of high failure rate is students rely too much on imprecise picture of shape instead of geometric rules that are always true. Learn the rules then use them.
Angle bisector theorem is out of syllabus and you don't need that. You should consider the area of △ABE and △DBE are the same (since AE = DE) (1/2)(AB)(BE)sinθ = (1/2)(BE)(BD)sinθ, θ is given equal, so AB = BD and it proves that △ABD is isoceles.
By alternate angles, angle BDE = angle CBD = x, then by isosceles triangle, BE = DE = AE and so angle BAE = x as well. Then x = 45 degrees. Hence I, II, and III are true. You dont need any extra info...
超正，條片，唔睇真係唔知！👍👍👍
Lui Eddie 加油！
So long as the order of vertices is ABCD, you can construct the parallelogram in any way you like and you still get the right conclusion despite awkward shapes. The steps: (1) let equal angles be x (2) angle BDE = x (alt angles // lines) (3) triangle BDE isosceles (base angles equal to x) (4) BE = DE (equal sides of isosceles triangle BDE) (5) triangle ABE isoceles triangle (equal sides BE = DE = AE as given) (6) angle BAE = x (base angles of isosceles triangle equal) (7) triangle ADB isosceles triangle (base angles equal to x) (8) AB = BD (equal sides of isoceles triangle ADB) (hence I correct) (9) angle sum of triangle ADB = 4x = 180 and given angle ABC = 3x = 135) (hence II correct) (10) triangle ABE and triangle DBE are congruent (SAS: AB = BD as equal sides of isosceles triangle ADB, common side BE, inclusive angles equal to x as given) (hence III correct). The whole derivation and conclusion are straight forward and independent of the shape drawn. Don't waste time searching for a correct shape. The actual reason of high failure rate is students rely too much on imprecise picture of shape instead of geometric rules that are always true. Learn the rules then use them.
呢題明顯考評局問題,喺知道平行四邊形ABCD嘅四點係喺順序逆時針嘅情況下,要知道答案係D完全冇難度
但問題係當你唔畫個平行四邊形出嚟,冇定義ABCD四點的時候,喺數學嘅角度唔應該假定佢四點嘅位置
而係要無論ABCD四點順序係點 個statement都正確 先可以話佢正確
出卷班教畜睇嚟已經唔記得左咩係數學
L Syrus 無人叫你 assume 斜邊係右上去左下😒
注意ABCD的次序代表四條邊由A接B,B接C,C接D,D接A是已經定義的,雖然沒有固定方向卻固定次序
即使是立體圖形也得按相鄰點來數
L Syrus
好明顯你未讀過數, 每個字母一定係表示順序畫出嚟嘅點同線豬西, 仲好意思出嚟7
L Syrus 自己渣 冇賴人啦 港孩
一看最少兩個對，同時I=III對，答案只有B和D。
X=角CBD=角BDA 平行四邊形
三角EBD是等邊三角
BE=AE=ED
角BAE=X
角BEA=2X
X+X+2X=180度
X=45度；角ABC=3X
III是對
其實...用prop. of isos. triangle就可以搞掂AB=BD這個問題，之後得出angle BED=90°(仍然是prop. of isos. triangle)
之後又是平行線性質，直接得出angle ABE=angle EBD=angle CBD=angle BDE=45°（會順手找出是一個直角等腰三角形），最後SSS,大功告成 xD
真的很容易,我也真的只是個F.2
*老實說，現在的考生最容易忽略的就是prop. of isos. triangle,學校一般都不會重點出那類題目，因為太難出。然而這條題目恰好用它是最好方法。
如何證明兩三角全等？
知唔知咩叫先要證左AB=BD先可以用prop of isosceles triangle...你既calculation 全部都係base on 未證既hypotheses,唔好誤導人啦😑
安德尊
Angle bisector theorem is out of syllabus and you don't need that.
You should consider the area of △ABE and △DBE are the same (since AE = DE)
(1/2)(AB)(BE)sinθ = (1/2)(BE)(BD)sinθ, θ is given equal, so AB = BD and it proves that △ABD is isoceles.
非常非常好👍
其實唔洗諗甘多奇怪野，直接隨手畫個平行四邊形，跟住就可以推嗮全部角出黎（全部都係簡單properties）
學過A-math/列陣式 先有機會知逆時針方向排字母,普通考生next 啦
順時針或者逆時針根本不影響答題
Ks Wong 但係識考慮排字母方向有絕對優勢喎
Gary Suen
順時針或者逆時針零影响, 零優勢, 事實上你鍾意可以將形狀反轉嚟諗, 有冇讀過所謂a math都可以, 但冇意思
完全唔關事，只要你順次序排就可以solve到
平行四邊形有咁多個，個個都arm少少，左邊嗰個arm d,右邊嗰個arm d啱咪係D，全部都arm
正常人都畫左手邊嘅平行四邊形啦，可以嗰15%考生係左手揸筆🤔🤔
其實如果I唔啱，II同III都唔啱
我做個時，証唔到I，但係如果I唔啱其實都錯，但冇non of the above ，所以好大機會係D
恍然大悟，謝謝。
d人從來冇諗過點解ass 證吾到全等
It is a good topic for our next video.
因為有條線可以180-x or x, 兩面擺
淨係要記得ASS證唔到全等都有好多人未做到
其實都唔難記既 以前我係記住ASS=屎忽=證唔到
理論上(A、S短、S長)應該證到(因為S長反唔到去另一面，等同底角Obtuse／Acute)，不過冇基本Reason可以用
逆時針方向呢條不明文規定係邊撚個整出嚟。。。（筋已青）
they dont have to be in counterclockwise direction. clockwise direction also ok, as long as they are in the right order
謝謝亞sir……
自資food science health care有伏，慎入
唔該晒安sir
thanks so much
這是什麼畫圖軟件？
Geogebra
哩個劃到個等邊三角形好緊要
當年我唔畫圖，憑空想像，三十秒就知道係D.
利申：2017DSE 數學5**
Cheng Marco 同意，只係一條好簡單既邏輯問題
可唔可以分享下thinking process
1 同 3係必定同時出現，所以只要諗2。AB=BD=DC，假設abe=cbd=dbe=x，bdc=2x, solve 2x+x+x=180,x=45,abc=3x=145
yik tao Chiu 呀～ 謝！
yik tao Chiu 點解 2x+x+x =180
好簡單
原來有伏
jack 戈
六年之前學的，全部忘光
thx
喔!長知識啦～
好心機
good
誠實得3, 不誠實5**！Yeah！
Wing Wong 😅😅😅