Constructing Perpendicular Bisectors: Use 4 different colors for the constructions below, 1 for each radius measure. The steps in the construction are outlined below. Step 1: Taking A and B as centers, and a radius more than half of AB, draw arcs on both sides of AB, to intersect each other, as shown below. Answer to By constructing the perpendicular bisectors of the. The reason you require the radius of your arcs to be more than ½ AB is that if the radius is less than ½ AB, the arcs will not intersect (try it!). Perpendicular bisector of a line segment Practise these constructions until you can do them without looking at the instructions. Construct perpendicular lines, including the perpendicular bisector of a line segment. Question: By constructing the perpendicular bisectors of the two given chords, detemnine the centre and radius of each of the circles. Think about the relationship between perpendicular bisectors and distance. on discussion of why they agree or disagree with responses. As a group, write answers to the questions. Step 2: Let the two points of intersection so obtained be P and Q. This is the required perpendicular bisector. Now, compare \(\Delta APO\) with \(\Delta BPO\):Ģ. \(\angle APO\) = \(\angle BPO\) (just shown)īy the SAS criterion, the two triangles are congruent, which means that AO = BO, and also: Proof: Compare \(\Delta PAQ\) and \(\Delta PBQ\):īy the SSS criterion, the two triangles are congruent, which means that \(\angle APO\) = \(\angle BPO\). ANSWERES TO GSP5 CONSTRUCTING PERPENDICULAR BISECTORS HOW TO.
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