UNIT 2 REVIEW GUIDE (CONSTRUCTIONS)
NAME ___________________________________________________PD _____ DATE ______________________
“There are no secrets to success. It is the result of preparation, hard work, and learning from failure.” –Colin Powell
COMPLETION Choose the BEST answer to complete each statement below.
_____
1. A geometric figure created with a straightedge and compass only is called a _____
a. construction
b. sketch
_____
2. If a point is on the perpendicular bisector of a segment, then it is ___________.
a. equidistant from the endpoints
b. divides the segment into two congruent
segments
_____
c. four congruent segments
d. a and b
6. Which point of concurrency is equidistant from the vertices of a triangle?
a. centroid
b circumcenter
_____
c. is the midpoint of the angle
d. all of the previous
5. When we construct the perpendicular bisector of a given segment, we obtain ___.
a. four congruent right angles
b two congruent segments
_____
c. along the segment bisector from the point to
the line
d. none of the previous
4. If a point is on the bisector of an angle, then it is ________________________.
a. equidistant from the sides of the angle
b. divides the angle into two congruent angles
_____
c. the midpoint of the segment
d. intersects the segment at its midpoint
3. The shortest distance from a point to a line is measured ___________________.
a. along the perpendicular segment from the
point to the line
b. along the angle bisector from the point to the
line
_____
c. drawing
d. all of the previous
c. incenter
d. orthocenter
7. Which point of concurrency is equidistant from the sides of the triangle?
a. centroid
b circumcenter
c. incenter
d. orthocenter
8. The length of the segment from the vertex of a triangle to the centroid is ____________
the length of the segment from the centroid to the midpoint of the opposite side.
PLANNING CONSTRUCTION OF ANGLES OF MANY SIZES Use what you know about duplicating angles
and bisecting angles, as well as how to construct 60 and 90 degree angles, to complete the chart below. Use this as a
resource to help you plan constructing (or describing how to construct) angles of many other sizes. Use your calculator.
9. EQUILATERAL 
10. PERPENDICULAR () LINES


60
90


______
______


______
______


______
______
11. Duplicate, by construction,  LUV below. Name your new angle  GEO.
L
U
V
12. Duplicate, by construction, the sum of the
measures of ’s A, B, and C from the triangle
below. Label your new angle as LRG. A
construction line and starting point have been
provided for you. Remember: Do NOT change
your compass setting while swinging arcs on each
angle. When you complete your construction,
complete the following: The measure of LRG =
________.
R
13. Using what is given in a-c below, construct perpendiculars.
a.
c.
Construct a perpendicular, given a point on a line:
f
b. Construct a perpendicular, given a
point NOT on a line:
Construct a perpendicular bisector, given a line segment:
14. MATCHING
15. Recall the definitions of each of the following before constructing them in  ABC provided
below. Construction Tip: It may be helpful to sketch a labeled diagram before actually constructing
the figure.
ANGLE BISECTOR
Sketch:
MEDIAN
Sketch:
Construction: Angle bisector
Construction: Median
BX
ALTITUDE
Sketch:
BM
Construction: Altitude
̅̅̅̅
𝑪𝑯
16. On a separate sheet, construct an equilateral triangle.
17. On a separate sheet, construct a square.
18. On a separate sheet, construct (using straightedge) a triangle. Then construct the following:
(1) incenter, (2) circumcenter, (3) orthocenter, and (4) centroid
Which three of these points are collinear? ___________________________________
The line through these three points is called the Euler Line. The Euler Line is named after the
Swiss mathematician Leonard Euler (1707-1783) who proved that the three points of
concurrency were collinear. Euler’s mathematical output was so tremendous that forty volumes of
his writings, representing just a small part of his work, have been published.
19. On a separate sheet, construct an isosceles triangle. (Apply your construction of an equilateral
triangle.) Make this triangle have exactly two congruent sides.
20. On a separate sheet construct angles with degree measure as indicated:
a. )
135 
b.) 15
21. Describe how to construct, step by step, angles with each of the measures below. HINT:
Using a chart (page two of study guide) may help you in putting your plan into words.
a. 120 ____________________________________________________________________
__________________________________________________________________________
b. 75 ____________________________________________________________________
__________________________________________________________________________
c. 22 ½  ___________________________________________________________________
_________________________________________________________________________
22. Point G is the centroid in each diagram below. Find the lengths of the segments listed below
using the given information.
a) GD=4
BG=6
AG=___ GE = ___
b)
AG=22 BE=21 GC=18
AD=___ GE = ___ FG=___
c)
AD=12 GE=5
AG=___ BE = ___