3. Use compasses straightedge to construct a perpendicular bisector of segment A

Question

3. Use compasses straightedge to construct a perpendicular bisector of segment AB and justify your construction. Justification: On the construction, quadrilateral APBQ is a kite, for and have the same radii. To validate your construction: by construction, i.e., in each of the both pairs , for (construction); ; and (construction); by SSS congruence condition. Therefore, 41 2 (CPCF) (mark the angles 1 and 2 on your construction) , for L2 (provedabove); and : by SAS congruence condition. (construction); _a_ Therefore, m· ; and (CPCF)·The construction is indeed a perpendicular bisector ofAB

Explanation / Answer

We have given line segment AB. We have to construct the perpendicular bisector of it using compass.

We follow the following steps to construct it ---

(1) First set your compass equal to three-fourth of length AB.

(2) First put the compass at A and cut two arcs at both side of AB.

(3) Same as cut two arcs from B also.

(4) Now match the two points where these arcs intersect.

So this line is your perpendicular bisector of AB.

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