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∆ABC ≅ ∆DEC supplementary ABC DEC ∠DEC non-included AAS ≅ Thm corresponding parts
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∠B ∠D ∠ACB ∠ECD BC DC ASA ≅ Post. ∆CDE DE
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Statements Reasons ∠PTS ≅ ∠QTS ∠SPR ≅ ∠RQS TS ≅ TR ∆PTS ≅ ∆QTR PT ≅ QT PT + TR = PR QT + TS = QS PR ≅ QS Given Vertical ∠'s Thm AAS ≅ Thm. 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.
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∠2 SAS ≅ Postulate (b/c AD ≅ AD by the Reflexive Prop.) ∆CED ∠CDE AAS ≅ Thm ∆CED AAS ≅ Thm ∆CED (CPCTC) SAS ≅ Post.
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GH ≅ KJ Given HJ ≅ JH Reflexive Prop. GH + HJ = GJ KJ + JH = KH Segment Addition Post. FG ≅ LK ∠FJG & ∠LHK are right ∠'s ∆FJK & ∆LHK are Right ∆'s Definition of Right ∆ GJ ≅ KH Definition of ≅ ∆FGJ ≅ ∆LHK HL Thm. FJ ≅ LH CPCTC ∠FJK ≅ ∠LHG ≅ Supplements Thm. ∆FJK ≅ ∆LHG SAS ≅ Post. Statements Reasons
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DE AC DF EF conclude DE DF EF A ∆FDE ∠A DE DF EF Given ∆FDE ∠A (CPCTC)
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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.
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