Angle Bisector Construction Using a Ruler and Compass
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Construction of the bisector of an angle using a ruler and a compass
Think and answer!
$1^{\circ}$ Draw an arc of a circle of center $O$. This arc cuts $[Ox)$ at $A$ and $[Oy)$ at $B$.
$2^{\circ}$ Draw two arcs of respective centers $A$ and $B$ and of same radius. These two arcs intersect at $I$.
$3^{\circ}$ The semi-line $[OI)$ is bisector of the angle $\widehat{xOy}$.
Measure the angles $\widehat{xOI}$ and $\widehat{yOI}$ to justify this construction.
Chapter 2 - Angles - Bisector of an angle
This question includes visual content: The image consists of three sequential diagrams illustrating the construction of an angle bisector. Diagram 1: Shows an angle $\widehat{xOy}$ with the needle of a compass at vertex $O$ drawing an arc that intersects ray $Ox$ at point $A$ and ray $Oy$ at point $B$. Diagram 2: Shows the same angle with the compass placed at point $B$ and then point $A$ to draw two intersecting arcs of equal radius. Diagram 3: Shows the final construction where a semi-line $[OI)$ is drawn from vertex $O$ through the intersection point $I$ of the two arcs from the previous step. The semi-line $[OI)$ represents the bisector.
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Step by Step Written Solution
In this activity, we will learn how to construct the bisector of an angle using only a ruler and a compass.
Construction of an Angle Bisector
Let's first look at step one. We start with an angle x O y. We use a compass to draw an arc centered at the vertex, O.
This arc intersects the two arms of the angle at points A and B. Because they are on the same arc, the segments OA and OB are equal in length.
Now for step two. Keeping the same compass width, or any fixed width, we draw two intersecting arcs centered at points A and B respectively.
The point where these two arcs intersect is labeled as point I.
Finally, in step three, we draw a semi-line starting from O and passing through I. This line is the bisector.
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