1. 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

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

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

4. 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

5. 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

6. 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

7. 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.

8. 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

9. 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

10. 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

11. 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)

12. 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

13. 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.