Someone Plz Help 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.

The measurement justifies the perpendicular bisector theorem

Step-by-step 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

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.