Constructing Angles Practice

Question

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Question
Use the image to answer the question.

Two rays diverge rightward from a vertex point labeled upper Q. One ray extends horizontally through a point labeled upper R, while the other extends diagonally through a point labeled upper P. Points upper R and upper P are connected by an arc.

On her paper, Katarzyna wants to construct the angle bisector of angle ∠PQR
. She has drawn an arc from the vertex point Q
that intersects both sides of the angle and has labeled the intersection of the arc with the sides of the angle with P
and R
. Using a compass and straightedge, what next step must she take to construct the angle bisector?

Option #1: Move the compass further apart and place the pointed end at point Q
and draw another arc that intersects the sides of the angle.

Option #2: Place the pointed end of the compass on point P
and draw another arc inside the first arc and between two sides of the angle.

Option #3: Place the pointed end of the compass on point P
and draw another arc outside the first arc and between two sides of the angle.

Option #4: Draw a line extending from the vertex point Q
through the middle of the angle.

(1 point)
Katarzyna’s next step is Option #
.

Answer 1

To construct the angle bisector after drawing the initial arc that intersects the sides of angle ∠PQR at points P and R, Katarzyna should place the pointed end of the compass on point P and draw another arc inside the first arc and between the two sides of the angle. This will allow her to find equal distances from point P to where the new arc intersects the sides of the angle.

Therefore, the correct next step for Katarzyna is:

Option #2: Place the pointed end of the compass on point P and draw another arc inside the first arc and between two sides of the angle.