Use the working space below. Draw the angle afresh; do not measure the teaching illustration. Keep a

Question

Use the working space below. Draw the angle afresh; do not measure the teaching illustration. Keep all construction arcs visible. Using a ruler and protractor, draw $\angle BAC=72^\circ$, with each arm at least $5$ cm long.[1] Now use a ruler and compasses only to construct the internal angle bisector. Label the equal-radius cut points on $AB$ and $AC$ as $D$ and $E$, and the intersection of the two further arcs inside the angle as $P$. Draw the ray $AP$.[2] Without measuring, state $\angle BAP$. Explain why your construction makes $\angle BAP=\angle PAC$, using congruent triangles.[3]

Accepted Answer

An accurate construction with three construction arcs retained. $\angle BAP=36^\circ$; the two triangles are congruent by SSS.

Constructing and justifying an angle bisector

Constructing and justifying an angle bisector

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