G. Tawfik          
MATHEMATICS 436

Extra-Review ER5 Geometry: Congruence of Triangles

                                Notes: see Geometry

                                Extra Practice ER5: Angles

                          Extra Practice ER5: Angles and Triangles

                          Practice # 3: Congruence of Triangles
 





1.    Prove that in rectangle ABCD,  < ABD = < CDB.







2.    In quadrilateral ABCD: < ABD = < BDC   and   < ADB = < DBC.
       Prove that   AB = CD





3.    Points B, F, E and D are points on a straight line as shown
       and BF = ED.
      A is a point above the line and C is a point below the line,
      such that:     AB = CD    and    AE = CF.
      Prove that   < A = < C






4.    Triangle ABC is isosceles and AC = BC.
       Point D is on AC and point E on BC so that: < CAE = < DBC
       Prove that AE = BD                                          



5.    Draw quadrilateral ABCD such that  E is the midpoint of BC
       AE = DE  and  < AEB = < DEC
       Prove that < B = < C




6.    Points X, Y, Z and W are points taken in this order on a circle with centre O
       so that     XY = ZW
       Prove that   < XOY = < ZOW


7.    Triangle PQR is isosceles with QP = QR.
       Point S is on QP, point T is on QR so that SP = TR.
       Prove that   < QPT = < QRS

8.    In triangle MNP and QNR:   MN = NQ       
                                                      NR = NP       
                                                     < MNP = < PNQ
       Prove that  < M = < Q