ABC DEC supplementary ABC DEC DEC nonincluded AAS
∆ABC ≅ ∆DEC supplementary ABC DEC ∠DEC non-included AAS ≅ Thm corresponding parts
∠B BC ∠D ∠ACB DC ∠ECD ASA ≅ Post. ∆CDE DE DE
Statements ∠SPR ≅ ∠RQS Reasons ∠PTS ≅ ∠QTS Given Vertical ∠'s Thm TS ≅ TR ∆PTS ≅ ∆QTR Given AAS ≅ Thm. PT ≅ QT PT + TR = PR QT + TS = QS PR ≅ QS CPCTC Segment Addition Post. Definition of ≅ Point D should be placed far enough away from B so that it's on land. This allows DE to be easily measured.
∠ 2 SAS ≅ Postulate (b/c AD ≅ AD by the Reflexive Prop. ) ∆CED ∠CDE AAS ≅ Thm ∆CED SAS ≅ Post. (CPCTC)
Statements Reasons GH ≅ KJ Given ∠FJG & ∠LHK are right ∠'s Given ∆FJK & ∆LHK are Right ∆'s HJ ≅ JH Definition of Right ∆ Reflexive Prop. GH + HJ = GJ KJ + JH = KH GJ ≅ KH FG ≅ LK ∆FGJ ≅ ∆LHK FJ ≅ LH ∠FJK ≅ ∠LHG ∆FJK ≅ ∆LHG Segment Addition Post. Definition of ≅ Given HL Thm. CPCTC ≅ Supplements Thm. SAS ≅ Post.
DE AC DF EF conclude DE DF EF A ∆FDE ∠ A DE Given DF EF ∆FDE ∠ A (CPCTC)
You know that AC ≅ AB and BD ≅ CD because they're determined by the same compass settings. Also, AD ≅ AD by the Reflexive Property. So, by the SSS congruence postulate, ∆CAD ≅ ∆BAD. Therefore, ∠CAD ≅ ∠BAD becuase corresponding parts of congruent triangles are congruent.
- Slides: 7