Consider a line ST with its line bisector below. U S T O From - PowerPoint PPT Presentation

D AY 66 – P ROPERTIES OF BISECTED LINE

I NTRODUCTION A farm owner may want to construct a path that passes exactly through the middle of his farm so enable access to various parts of the farm. The problem will be how to identify a line that divides the real estate into two equal portions. A bisector of a line equivalent to the length of the farm will pass through the middle of the estate. This is the case when the farm is rectangular or square shaped. In this lesson, we are going to show that a bisector of a line divides it into two equal proportions.

V OCABULARY Mid-point This is a point on line that divides the line into two halves. Bisector of a line A point or a line that divides a line at its midpoint.

Consider a line ST with its line bisector below. U S T O

From the definition of a line bisector, OU passes through the midpoint of ST. Thus SO and TO are congruently implying that 𝑇𝑃 = 𝑈𝑃 Thus the bisector divides line ST into two equal portions. The length of the line is twice the length one portion. The following equations hold with respect to line ST, 𝑇𝑈 = 2𝑇𝑃, 𝑇𝑈 = 2𝑈𝑃, 2 𝑇𝑈 = 𝑇𝑃 = 𝑈𝑃 . 1 Note that a bisector of a line divides it into a ratio of 1:1.

Example A bisector of line MN is drawn such that the distance from M to midpoint is 3.2in. What is the length of line MN? Solution The bisector divides line MN into two equal portions. One portion has a length of 3.2in, Thus MN = 3.2 × 2 = 6.4𝑗𝑜

HOMEWORK Line AB is bisected such that the bisector passes through point P on AB. If the length of AB is 5 in, what is the length of BP?

A NSWERS TO HOMEWORK 2.5in

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