as ab=ln and angle b = angle n - corbettmaths · pdf filewe do not know exact location of each...
TRANSCRIPT
![Page 1: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/1.jpg)
![Page 2: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/2.jpg)
As AB=LN and Angle B = Angle NThen Angle A = Angle L
![Page 3: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/3.jpg)
![Page 4: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/4.jpg)
![Page 5: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/5.jpg)
We do not know exact location of each angle. The two triangles above are not congruent
BD is sharedBA = CD (opposite sides of a parallelogram)BC = AD (opposite sides of a parallelogram)Therefore ABD and BCD are congruent due to Side, Side, Side.
![Page 6: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/6.jpg)
Depends on values found.Could be SSS/SAS/RHS/ASA etc
![Page 7: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/7.jpg)
DG = EF as rhombus (opposite sides)DH = HF diagonals bisect each otherGH = EH diagonals bisect each otherDGH and EFH are congruent as SSS
![Page 8: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/8.jpg)
CD = FE (given)Angle DCE = FEC (alternate angles)Angle CDF = EFD (alternate angles)CDG and EFG are congruent as ASA
![Page 9: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/9.jpg)
DG is sharedDF = DE as equilateral triangleAngle DGE = DGF = 90 degreesTherefore congruent as RHS.
Or Angle EFD = FED = 60 degrees as equilateral triangle.Therefore both EDG = FDG = 30 degreesSo could say SAS.
Or even AAS or ASA
Clear explanation needed
![Page 10: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/10.jpg)
AC = BC (sides of an isosceles triangle)Angle ACD = BCE (shared)CE = CD (given)Therefore SAS.
![Page 11: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/11.jpg)
1) Angles BLC = AOB = 90 degrees as LMNO is a square.2) Angle ABL = 90 - x as ABC is a right angle and CBL = x3) Angle BCL = 90 - x as angles in a triangle add to 180 and Angle CBL = x and Angle BLC = 90.4) Angle OAB = x as angles in a triangle add to 180 and Angle ABL = 90 - x and Angle AOB = 90.5) AB = BC as a square.
Congruent as ASA.
![Page 12: As AB=LN and Angle B = Angle N - Corbettmaths · PDF fileWe do not know exact location of each angle. The two triangles above are not congruent BD is shared BA = CD (opposite sides](https://reader031.vdocument.in/reader031/viewer/2022030412/5a9e5acc7f8b9a0d7f8d9ae3/html5/thumbnails/12.jpg)
AB = AD as a squareBAC = ADB = 45 degrees (diagonals bisect right angle)Let ABY = xTherefore AYB = 180 - 45 - x = 135 - xEYF = AYB (vertically opposite)AEB = XEB = 90 degrees (perpendicular as in Question)Four right angles at F (diagonals of a square)XEYF is a kite and since XEY = XFY = 90, then EYF and EXF add to 180. So EXF = 45 + xTherefore DXA = 135 - x (angles on straight line add to 180)As angles in AXD add to 180, DAX = xTherefore!! AYB is congruent to AXD due to Angle/Side/Angle
EF