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Sagot :
The angle bisector QS is constructed using arcs of the same width
intersecting above the segment joining equidistant point from Q.
Correct Response;
- c. ∠AQS ≅ ∠BQS when AS = BS and AQ = BQ
Reasons why the selected option is correct;
The steps to construct an angle bisector are as follows;
- Draw an arc from the vertex of the angle, Q, intersecting the rays forming the angle, QP and QR, at points A and B respectively.
- From points A, and B, draw arcs having same radii to intersect between the rays QP and QR at point S.
- Join the point of intersection of the small arcs at S to Q to bisect the angle PQR.
The reason why Ben uses the same width to draw arcs from A and B is as follows;
The point A and B are equidistant from point Q, therefore, point Q is point of intersection of arcs of radius AQ = BQ drawn from A and B.
Similarly point S is the point of intersection of arcs AS = BS from points A and B.
Which gives that the line QS is the perpendicular bisector of the segment AB, where ΔABQ is an isosceles triangle, therefore, QS bisects vertex angle ∠PQR.
Therefore, the correct option is the option c.;
- c. ∠AQS ≅ ∠BQS when AS = BS and AQ = BQ
Learn more about angle bisector here:
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