Problem

Copy angle \(ABC\) at endpoint \(P\) of ray \(PX\). A \(B\)-centered source arc meets the angle rays at \(Q\) and \(R\), and the matching \(P\)-centered target arc meets ray \(PX\) at \(S\). Complete the angle copy by stating the target-arc action, chord transfer and center, target intersection, final ray, and congruence result.

Big Picture

What this problem is really about

Copying an angle means reproducing its geometry, and a radius alone does not record how wide the angle opens. We’ll transfer both the source arc radius and the chord between its ray intersections, then use the matching three lengths to prove that the target central angle matches the source.

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target arc = copy source arc radius at P and mark S on PX; chord transfer = set compass to QR and center at S; target intersection = K on target arc; final ray = PK; result = angle at P equals angle ABC

target arc = copy radius at P, mark S; chord transfer = QR at S; target intersection = K undefined; final ray = PK first; result = congruent

target arc = copy radius at P, mark S; chord transfer = QR but change target radius; target intersection = K; final ray = PK; result = congruent

target arc = copy radius at P, mark S; chord transfer = QR centered at P; target intersection = K; final ray = PK; result = congruent

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