Proving the perpendicular bisector theoremīehold the awesome power of the two words, "perpendicular bisector," because with only a line segment, HM, and its perpendicular bisector, WA, we can prove this theorem. You repeat the operation at the 200 meter height, and the 100 meter height.įor every height you choose, you will cut guy wires of identical lengths for the left and right side of your radio tower, because the tower is the perpendicular bisector of your land. You need guy wires a whopping 583.095 meters long to run from the top of the tower to the edge of your land. Use the Pythagorean Theorem for right triangles: One measurement, which you can calculate using geometry, is enough. How long should a guy wire from the top down to the land be, on each side?īecause you constructed a perpendicular bisector, you do not need to measure on each side. You need to reinforce the tower with wires to keep it from tipping over in high winds. Your radio tower is a perpendicular bisector of the length of your land. You plan to broadcast rock music day and night.Īnyway, that location for your radio tower means you have 500 meters of land to the left, and 500 meters of land to the right. You built a humdinger of a radio tower, 300 meters high, right smack in the middle of your land. Suppose you have a big, square plot of land, 1,000 meters on a side.
Perpendicular Bisector Theorem Definition How does it work? If a point is on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment. So putting everything together, what does the Perpendicular Bisector Theorem say? What Does Perpendicular and Bisector Mean? Perpendicular bisector theorem Putting the two meanings together, we get the concept of a perpendicular bisector, a line, ray or line segment that bisects an angle or line segment at a right angle.īefore you get all bothered about it being a perpendicular bisector of an angle, consider: what is the measure of a straight angle? 180☁80° that means a line dividing that angle into two equal parts and forming two right angles is a perpendicular bisector of the angle. A bisector cannot bisect a line, because by definition a line is infinite. BisectorĪ bisector is an object (a line, a ray, or line segment) that cuts another object (an angle, a line segment) into two equal parts. A line is perpendicular if it intersects another line and creates right angles. Perpendicular means two line segments, rays, lines or any combination of those that meet at right angles. since congruent angles are angles of equal measure.All good learning begins with vocabulary, so we will focus on the two important words of the theorem.We have established that the rays forming these angles coincide under a reflection. The reflection of ∠ CAB will have the same measure as ∠ CBA since reflections preserve angle measure.The reflections of and the reflection of.The reflection of A is B since reflections preserve length and the segments share point C.The reflection of will have the same length as that of.Since these angles are equal in measure, the reflection of ray (side of the ∠) will coincide with its image.Since m∠ACD = m∠BCD and reflections preserve angle measure, the image of ∠ ACD will be the same measure as ∠ BCD.Under a reflection in, the reflection of C will be C, since C lies on the line of.m∠ACD = m∠BCD because an angle bisector forms two congruent angles which have equal measure.Label the intersection with the base as D. Construct an auxiliary line through point C bisecting ∠ C.
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