Multiple Choice Practice Constructions Geometry Level Geometry Index | Regents Exam Prep Center

 Also available in Hardcopy (.pdf): Constructions

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.

1.   When finished with the construction for "Copy an Angle", segments are drawn connecting where the arcs cross the sides of the angles.  What method proves these two triangles to be congruent?
[1]  ASA                [2]  ASA                   [3]  SSS                 [4]  AAS

2.  According to the construction shown in the diagram below,  what do we call segment ?

[1]  bisector of angle C
[2]  median to side
[3]  perpendicular bisector of segment
[4]  altitude to side

3.  The point where the medians of a triangle are concurrent is called the

[1] centroid      [2]  orthocenter        [3]  incenter          [4]  circumcenter

4.  The centroid of a triangle divides the medians into ratios of

[1]  2:1            [2]  3:1                   [3]  4:1                  [4]  5:1

5.  The circumcenter of an acute triangle is located inside the triangle.  The circumcenter of an obtuse triangle is located outside the triangle.  Where is the circumcenter of a right triangle located in relation to the triangle?

[1]  on the triangle
[2]  outside the triangle
[3]  inside the triangle
[4]  the location varies

 6.  Scalene triangle ABC is shown at the right.  The distance from the centroid of a triangle to the circumcenter is 6 units.  How far is the centroid from the orthocenter?       [1]  8      [2]  12      [3]  16      [4]  24

7.  You are looking at a triangle where the orthocenter, the centroid and the circumcenter are all the same point.  What type of triangle are you looking at?

[1]  scalene                [2]  isosceles            [3]  equilateral           [4]  right

8.  When constructing the bisector of a line segment, you are also constructing the perpendicular bisector of the segment.

[1]  TRUE               [2]  FALSE

9.  When constructing a line parallel to a given line, you will be

[1]  copying a segment.
[2]  bisecting a segment.
[3]  copying an angle.
[4]  constructing a perpendicular

10.  The orthocenter of a triangle is always located inside the triangle.

[1]  TRUE          [2]  FALSE

11.  It is possible to inscribe a circle in any shaped quadrilateral.

[1]  TRUE          [2]  FALSE

12.  The point of concurrence of the angle bisectors of a triangle is always located inside the triangle.

[1]  TRUE           [2]  FALSE

13.  The point of concurrence of the perpendicular bisectors of a triangle is always located inside the triangle.

[1]  TRUE           [2]  FALSE

14.  One method of constructing an equilateral triangle is to simply construct a triangle using the same segment for each side.

[1]   TRUE          [2]  FALSE

15.  In relation to constructions, a straightedge is

[1]  a clear plastic device devoid of markings.
[2]  often shaped like a triangle.
[3]  used for drawing straight lines or segments, but not for measuring.
[4]  all of the above.

16.  You are asked to "construct" an angle whose measure is 30°.  Which of the following methods would be considered an acceptable construction?

[1] Using a protractor, draw an angle of 30°.
[2] Using a compass and straightedge, construct an equilateral triangle and then bisect
one of its angles.
[3] Using a compass and straightedge, copy an angle that appears to be close to 30°
from a diagram in your textbook.
[4] Using a compass and straightedge, construct two parallel lines and label one of
the angles 30°.

17.  The centroid of a triangle is located 12 units from one of the vertices of a triangle.  Find the length of the median of the triangle drawn from that same vertex.

[1] 16                    [2] 18                     [3] 24                      [4] 36

 18.  Which construction is shown in the accompanying diagram?      [1]      [2]       [3]           [4]

19.  Which diagram below shows a correct mathematical construction using only a compass and a straightedge to bisect an angle?

[1]
[2]
[3]
[4]

20.  When given a square, the construction of an angle bisector at any vertex will create the diagonal of the square.

[1] TRUE            [2] FALSE