Place the compass needle at point X and open the compass to a radius greater than half the length of side XY.

Question

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Here are the instructions for parts b, c, and d, continuing from your previous construction of triangle XYZ. b) To construct the perpendicular bisector of side XY: Step 1: Place the compass needle at point X and open the compass to a radius greater than half the length of side XY. Step 2: Draw an arc above and below the line segment XY. Step 3: Without changing the compass opening, place the compass needle at point Y and draw another set of arcs above and below XY, ensuring they intersect the first set of arcs. Step 4: Draw a straight line connecting the two points where the arcs intersect. This line is the perpendicular bisector of side XY. c) To construct the perpendicular bisector of side XZ: Step 1: Place the compass needle at point X and open the compass to a radius greater than half the length of side XZ. Step 2: Draw an arc above and below the line segment XZ. Step 3: Without changing the compass opening, place the compass needle at point Z and draw another set of arcs above and below XZ, ensuring they intersect the first set of arcs. Step 4: Draw a straight line connecting the two points where the arcs intersect. This line is the perpendicular bisector of side XZ. d) What do you notice? You will notice that the perpendicular bisector of the base XZ passes through the vertex Y. Also, the perpendicular bisectors of all three sides (XY, YZ, and XZ) will intersect at a single point, which is the circumcenter of the triangle.

Place the compass needle at point X and open the compass to a radius greater than half the length of side XY.

Step-by-step solution

Part b· 4 steps

Place the compass needle at point X and open the compass to a radius greater than half the length of side XY.

Draw an arc above and below the line segment XY.

Without changing the compass opening, place the compass needle at point Y and draw another set of arcs above and below XY, ensuring they intersect the first set of arcs.

Draw a straight line connecting the two points where the arcs intersect.

Part c· 4 steps

Place the compass needle at point X and open the compass to a radius greater than half the length of side XZ.

Draw an arc above and below the line segment XZ.

Without changing the compass opening, place the compass needle at point Z and draw another set of arcs above and below XZ, ensuring they intersect the first set of arcs.

Draw a straight line connecting the two points where the arcs intersect.

Part d

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