Question

draw a diagram that shows real - situation that applies perpendicular and angle bisector. label them and provide a short description.

Explanation:

A perpendicular bisector is a line that intersects another line segment at a right angle (90 degrees) and divides it into two equal parts. An angle bisector is a line that divides an angle into two equal smaller angles. For a real - situation example, consider a triangular park. Suppose we have a triangular - shaped plot of land (triangle ABC). If we want to build a pathway that is the perpendicular bisector of one of its sides (say side AB). This pathway will start from the mid - point of AB and be perpendicular to AB. It can be used for symmetry in landscaping or for a balanced distribution of resources (like placing a water fountain at the mid - point along the perpendicular bisector). For an angle bisector, if we have a corner (angle) of a building (say angle at a corner of a rectangular - like building extension which is an angle, and we want to install a light fixture that illuminates both adjacent walls equally. The light fixture should be placed along the angle bisector of that corner angle.

Answer:

For the perpendicular bisector: Draw a line segment \(AB\). Mark its mid - point \(M\). Then draw a line \(CD\) passing through \(M\) and perpendicular to \(AB\). Label \(AB\) as the original segment, \(M\) as the mid - point, and \(CD\) as the perpendicular bisector. For the angle bisector: Draw an angle \(\angle XYZ\). Using a compass, construct a ray \(YW\) such that \(\angle XYW=\angle WYZ\). Label \(\angle XYZ\) as the original angle and \(YW\) as the angle bisector.