What does that look like? We hope you said Side Angle Side, because that is exactly what it is. What do we have now? We have two right triangles, W H A and W A M, sharing side W A, with all these congruences: This means, if we run a line segment from P o i n t W to P o i n t H, we can create right triangle W H A, and another line segment W M creates right triangle W A M. That line bisected H M at 90 ° because it is a given. We are given line segment H M and we have bisected it (divided it exactly in two) by a line W A. Proving the Perpendicular Bisector Theoremīehold the awesome power of the two words, "perpendicular bisector," because with only a line segment, H M, and its perpendicular bisector, W A, we can prove this theorem. You repeat the operation at the 200 m e t e r height, and the 100 m e t e r 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 m e t e r s long to run from the top of the tower to the edge of your land. You can go out 500 m e t e r s to anchor the wire's end. So putting everything together, what does the Perpendicular Bisector Theorem say? 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 ° 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. A line is perpendicular if it intersects another line and creates right angles.Ī bisector is an object (a line, a ray, or line segment) that cuts another object (an angle, a line segment) into two equal parts. Perpendicular means two line segments, rays, lines or any combination of those that meet at right angles. Segment CD is congruent to segment AB.Perpendicular Bisector Theorem (Proof, Converse, & Examples)Īll good learning begins with vocabulary, so we will focus on the two important words of the theorem. Label the point where the arc intersects the ray point D. Stage 3: Without changing the opening of your compass, put the sharp end of your compass on point C and make an arc on the ray. Open the compass until the other end touches point B, and make an arc. Stage 2: Put the sharp end of your compass on point A. Stage 1: Draw a ray that extends longer than AB and label the endpoint C. Step 1 shows the three stages involved in duplicating segment AB. Try constructing CD on your own before looking at Step 1 of the investigation in your book. Now think about how you can use only your compass to create a segment, CD, that is the same length as AB. Draw a ray on your paper that extends longer than AB. When you construct a figure, you may use a ruler as a straightedge, but not as a measuring tool. Investigation 1: Duplicating a Segment In this investigation you will copy this segment using only a compass and straightedge. You can read about the history of constructions in the lesson introduction in your book. In this lesson you will focus on constructions. As with compass-and-straightedge constructions, patty-paper constructions do not use measuring tools. You can also construct a figure using patty paper and a straightedge.Compass-and-straightedge constructions allow you to accurately draw congruent segments and angles, segment and angle bisectors, and parallel and perpendicular lines. When you make a construction, do not use your measuring tools. You can construct a figure using a compass and straightedge.Make a drawing when it is important for lengths and angle measures to be precise. You can draw a figure using measuring tools, such as a protractor and a ruler.Make a sketch when exact measurements are not important. You can sketch a figure without using geometry tools.Duplicate an angle by using a straightedge and a compass and by using patty paper and a straightedge In geometry, there are several methods for creating a figure.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |