HUSKY STUDY BUDDY!
Geometry Regents Review
Session 2-May 18
th
2016
Constructions and Similarity
Part 1: Constructions- There will definitely be a construction on the Regents Exam, you MUST
practice with your compass and straight edge memorize the steps of all of the following constructions.
Some are basic and some take a few more steps.
Basic Constructions:
Check List (check when you’ve mastered the construction
1. Copy a line Segment
2. Copy and angle
3. Bisect a line segment ( use perpendicular bisector)
4. Bisect an angle
5. Perpendicular lines( use perpendicular bisector)
6. Parallel Lines
7. Equilateral triangle.
Many times the regents will have you construct a more complex construction that require two
constructions we have learned within one problem!
Here are some examples of complex constructions we’ve seen: (Note: constructions are not limited to this
list):
Complex Constructions (require several basic constructions)
1. Inscribed Regular Hexagon and Inscribed equilateral triangle.
2. Construct an inscribed Square.
3. Constructing a Circumscribed circle ( or inscribed triangle)
4. Constructing a square with given side length.
5. Construct a 30 degree angle.
6. Construct a 45 degree angle.
7. Constructing an inscribed circle.
8. Medians and Altitudes
9. Points of Concurrency
Check List (check when you’ve mastered the construction
Go to this site for step by step videos!
Regents-Style Questions
June 2015:
August 2015:
These are the constructions we’ve seen in the last three regents Exams, let’s do them together!
January 2016:
Constructions Practice
Construct a 45 degree angle
Construct a Square
Construct an altitude in a triangle
extending through A
Construct a median in a triangle
extending through P
Constructions Steps and Picture Steps Cheat Sheets
Perpendicular Bisector
Copy an Angle
Angle Bisector
Perpendicular to a point
Parallel to a given line through a given
point
Equilateral Triangle
Regular Hexagon
Step #1:
1. Create a circle with center O.
Take your ruler and a pencil and construct a
segment of any length on a piece of paper
as shown below
Then, you will try to set your compass
opening to match the length of segment AB
2. Mark a point anywhere on
the circle with the compass
centered at O. You now have
measured the radius of the
circle and the marked point
will be the first vertex of the
hexagon.
Take your compass. Make your sure that the
pencil is included in it.
Put the needle of the compass at endpoint A
and adjust your compass so that the tip of
your pencil touches endpoint B
3. Make a small arc at the point
marked in step 2.
Step #2:
Put the needle of your compass at A and
draw an arc. Put the needle of your compass
at B and draw an arc
4. Using the same width of the
compasses, move the
compasses needle point
onto the arc created in step
3, and draw another arc on
the circle. This is the second
vertex of the hexagon.
5. Continue this process until
you have all six vertices.
6.
Step #3:
Draw the segments from the two endpoints
to the point where the two arcs intersects
Draw a line between each
successive pairs of vertices,
for a total of six lines.
We are done. These lines form a
regular hexagon inscribed in a
circle.
(Pictures)
Practice!
1. Construct 30 degree angle with vertex at C
4. Construct a parallel line through p
2. Construct the centroid of the triangle below
3. Construct an angle bisector
5. Construct a hexagon inscribed in the circle below
6. Construct a line perpendicular to the given line through point p
Hint: Extend line m
7. Construct a square inscribed in circle O
*IF you would like more practice, ask your Geometry teacher for other constructions to try on your own or at extra help 