Review Sheet Constructions Required Constructions: G-4 SOL The student will construct and justify the constructions of a) a line segment congruent to a given line segment; b) the perpendicular bisector of a line segment; c) a perpendicular to a given line from a point not on the line; d) a perpendicular to a given line at a given point on the line; (or a tangent to the circle at the endpoint of a radius; tangent is perpendicular () to the radius) e) the bisector of a given angle, f) an angle congruent to a given angle; and g) a line parallel to a given line through a point not on the given line. Key Concepts: Remember we are using equal distance concepts to draw these. All Bisectors are from properties of Rhombi (all sides equal) Diagonals of Rhombi are perpendicular to and bisect each other Diagonals of Rhombi are angle bisectors of opposite angles Perpendiculars (bisectors and through points) are drawing isosceles triangles (or rhombi) Parallel line is constructing alternate interior angles (that are congruent with parallel lines) Test Taking Tips: Find equal distances Need to look at each set of instructions in case they ask about the instructions (justify) Eliminate answers that don’t make sense with the picture

First step is to create two points on the line segment equal distance from point P

They are asking to construct an angle bisector and match with an answer.

drawing an angle congruent to another Lines and Angles SSM: must be with angles two separate angles copy an angle drawing an angle congruent to another

must involve perpendicular eliminates A Lines and Angles SSM: must involve perpendicular eliminates A need two arcs crossing line equidistant from point need an arc from each of those intersection points on the other side of the line

Our eyes tell us that ABD and DBC are equal Lines and Angles SSM: Our eyes tell us that ABD and DBC are equal Construction is an angle bisector ABC is the whole and ABD and CBD are the halves

measure ST to find midpoint use ruler to line up perpendicular Ch C Coordinate Relations and Transformations SSM: measure ST to find midpoint use ruler to line up perpendicular Use compass to measure the same length arc from point S above and below. do the same from point T. Connect the intersections.

eliminate answers that don’t make sense Ch C Coordinate Relations and Transformations SSM: big arc centered at D eliminate answers that don’t make sense Constructions marks are a bisection of angle D

use ruler to measure “mouth” Ch C Coordinate Relations and Transformations SSM: use ruler to measure “mouth” Draw an arc centered at A. Draw same length arc centered at B. Measure the distance from intersection on the lower ray to the upper ray with A Create same length arc on B from intersection on lower arc

eliminate answers that do not fit Ch C Coordinate Relations and Transformations SSM: eliminate answers that do not fit Point p is not on the line and the line through it is perpendicular. No line segments are present

two arcs are same in the two pictures Ch C Reasoning, Lines, and Transformations SSM: two arcs are same in the two pictures first picture is an angle or two segments No evidence of angles cut in half; line segment not copied to length Nothing on the other side of line segment (for perpendicular)

Use eyes to evaluate and eliminate incorrect answers Ch C Reasoning, Lines, and Transformations SSM: Use eyes to evaluate and eliminate incorrect answers One line is a partial circle around g Second set of arcs are from the end points

use ruler on computer to measure Ch C Reasoning, Lines, and Transformations SSM: use ruler on computer to measure Use the compass to mark the distance between M and P. Keep that distance and draw two arcs from T and S. Which ever one intersects a point at the top is the answer.