Be able to identify which triangles can be constructed by the methods: SSS, SAS, AAS, ASA, SsA, or HL. Be able to construct those triangles that can be constructed and identify the method. 1. Construct  ABC with 2. Construct  DEF with AB = 3”, BC = 2”, CA = 3  ”DE = 3”, m  E=86 , EF = 2” 3. Construct  GHI with 4. Construct  JKL with m  G=35 , GH = 3”, HI = 2” m  L=59 , KL = 2”, JK = 3” Your exam will be on _________________ You may use the study guide on the exam only if you have completed every problem. Constructing & Proving Congruent Triangles Study Guide Name:____________________ p.1 Hint: SSSHint: SAS Hint: ASS Hint: SsA

5. Construct  MNO with 6. Construct  PRQ with m  M=35 , MN = 3”, m  N=86 , PR = 3”, m  R=86 , m  Q=59  7. Construct  STU with 8. Construct  VYX with m  S=35 , m  T=86 , m  U=59  m  V=90 , XV = 4”, YX = 5” p.2 Hint: ASAHint: AAS Hint: AAA Hint: SsA or HL

Name the two pair of alternate interior angles: ___________ & ___________ and ___________ & ___________ Name the vertical angles in the triangles: ___________& ___________ Name the side included by  VPR and  V :__________ You may use the study guide on the exam only if you have completed every problem. Name the pair of congruent angles created if GH bisectors  QGR: _______________ & _________________ Name the pair of congruent angles created if GH bisectors  QHR: _______________ & _________________ Name the angle included by QH and QG: __________ Name the pair of congruent segments created if W is the midpoint of OT: _______________ & _________________ Name the vertical angles in the triangles: ___________& ___________ Name the angle opposite BO: __________ Name the side opposite  I:___________ p.3

Name the right angles formed BE  AD: _______________ & _________________ Name the right angles formed AE  CD: _______________ & _________________ Name the part in the overlapping triangles that is congruent to itself by Reflexive Property. _______________ B C A D E Name the pair of congruent segments created if N is the midpoint of JK: _______________ & _________________ Name the part in both triangles that is congruent to itself by Reflexive Property. _______________ Name the hypotenuse: ______________________________ Name the legs: ____________________________________ Which pair of triangles can be assumed congruent by SsA? ________ A.B. Write the congruence statement for those triangles. ______________________________________ p.4

You may use the study guide on the exam only if you have completed every problem. Copy the SSS congruence theorem: Find and copy or complete this proof: Copy the SAS congruence theorem Find and copy or complete this proof: Given: XA = YA and XC = YC Prove:  XAC  YAC A Y C X p.5 Hint: to prove ∆XAC  ∆YAC apply reflexive property & SSS To  XAC  YAC apply CPCF Hint: to prove ∆JUE  ∆ILU apply vertical angles & SAS To JE  LI apply CPCF

You may use the study guide on the exam only if you have completed every problem. Copy the ASA congruence theorem: Find and copy or complete this proof: Copy the AAS congruence theorem: Find and copy or complete this proof: Given: m  ADB = m  CDB m  ABD = m  CBD Prove: AB = CB B C A D p.6 Hint: to prove ∆ABD  ∆CBD apply reflexive property & ASA To AB =CB apply CPCF Hint: to prove ∆PRS  ∆TQR apply reflexive property & AAS

Given: ON > OG, ON  FE OG  GE To prove:  GNO   GFE You may use the study guide on the exam only if you have completed every problem. Copy the SsA congruence theorem: Find and copy or complete this proof: Copy the HL congruence theorem: Find and copy or complete this proof: Given: VX  WY and WZ = VY XZ = XY Prove:  W   V WY V X Z p.7 Hint: to prove ∆GNO  ∆GFE vertical angles & SsA Hint: to prove ∆WXZ  ∆VXY apply HL or SsA To  W  V apply CPCF