27. Given:TwSw>SwFw>FwHw>HwTw/TSF,/SFH,/FHT, and/HTSare right angles.Prove:/SHT>/SHFProof:28. Given:DwEw>FwBw,AwEw>FwCw,AwEw'DwBw,CwFw'DwBwProve:nABD >nCDBPlan:First use SAS to show that nADE>nCBF.Next use CPCTC and Reflexive Property forsegments to show nABD>nCDB.Proof:29.Sample answer: The properties of congruenttriangles help land surveyors double checkmeasurements. Answers should include thefollowing.• If each pair of corresponding angles and sidesare congruent, the triangles are congruent bydefinition. If two pairs of corresponding sidesand the included angle are congruent, thetriangles are congruent by SAS. If each pair ofcorresponding sides are congruent, the trianglesare congruent by SSS.• Sample answer: Architects also use congruenttriangles when designing buildings.30.C; using vertical angles and exterior angles,a1b590. Given this fact, it is impossible for theother statements to be true.
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