Question

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Draw AB and construct its perpendicular bisector. Identify point C on the bisector. Measure the distance from point C to point A and from point C to point B. What theorem does your measurement justify? Explain your answer.

Answer 1

The measurement justifies the perpendicular bisector theorem

Explanation:

Mathematically, what the theorem is saying is that the distance AC is the same as the distance BC

This is because. the line joining both points is coming from the same external point which is on the bisector of the line joining the two points.

Hence, what we are sayingg here is that the lines coming from the point C which is a point on the perpendicular bisector of the line segment AC is equal for both end points on the line segment.

Thus, by measuring both lines, we can see that they are congruent and the triangle we have is an isosceles triangle