1
GEOMETRY LESSON 1-5 BASIC CONSTRUCTIONS
1) According to the construction shown in the diagram below, what do we call
segment
?
a) bisector of angle C
b) median to side AB
c) perpendicular bisector of segment AB
d) altitude to side AB
2) Given: angle A .What is the first step in constructing the angle bisector of angle A?
A Draw ray AD .
B Draw a line segment connecting points B and C.
C From points B and C, draw equal arcs that intersect at D.
D From point A, draw an arc that intersects the sides of the angle at points B and
3) Marsha is using a straightedge and compass to do the construction shown below
1
2
Which best describes the construction Marsha is doing?
A a line through P parallel to line l
B a line through P intersecting line l
C a line through P congruent to line l
D a line through P perpendicular to line
4) Scott is constructing a line perpendicular to line l from point P. Which of the following
should be his first step?
A)
B)
C)
D)
5) Which triangle can be constructed using the following steps
1. Put the tip of the compass on point A.
2. Open the compass so that the pencil tip is on point B.
3. Draw an arc above AB .
4. Without changing the opening, put the metal tip on point B and draw an arc
intersecting the first arc at point C.
6) Draw AC and BC
2
3
A) right
B) obtuse
C)scalene
D) equilateral
7) What geometric construction is shown in the diagram below
A an angle bisector
B a line parallel to a given line
C an angle congruent to a given angle
D a perpendicular bisector of a segment
8) True or False, all segments have a perpendicular bisector.
A) true
b) false
9) What is the first step in constructing an angle bisector?
A) Draw a ray.
B) Label the points of intersection.
C) Measure the line.
*D) Place the compass point on the vertex.
10) What is the first step in constructing a congruent segment?
A) Set the compass length.
C) Place the compass on the ray.
*B) Draw a ray.
D) Label the point of intersection.
11) True or False, a perpendicular bisector must be the same length as the segment it
bisects.
A)true
b) False
3
4
12) If the bisector of ST intersects at point N, and ST is 8 in., what is NT
a) 6 in
b) 4 in
c) 16 in
d) 12 in
13) In the figure (not drawn to scale), MO bisects  LMN , m  NMO  6 x  19 °,
0
and m  LMO  9 x  140 . Solve for x and find  LMN .
a) 11, 198°
b) 11, 170°
c) 8, 25°
d) 8, 54°
14) SQ bisects  RST . Find the measure of  RST if m  QST  450
a) 40°
b) 100°
c) 45°
d) 90°
15) In the figure shown, name the ray that appears to bisect  JKL .
a)
b)
c)
d)
16) Which diagram is a step in bisecting m  MAC ?
4
5
A)
b)
c)
d)
17) In which figure is SV a perpendicular bisector
a)
b)
c)
d)
18) What is the value of x in the figure below?
5
6
a)37.5
b)42,5
c)47.5
d)62.5
19) In the figure below, line SZ  line XG
Which pair of angles are adjacent and complementary?
a)  XKS and  GKS
c)  YKS and  ZKT
*b)  XKY and  ZKY
d)  XKZ and  GKS
20) You are asked to "construct" an angle whose measure is 30°. Which of the following
methods would be considered an acceptable construction?
A) Using a protractor, draw an angle of 30°.
B) Using a compass and straightedge, construct an equilateral triangle and then bisect
one of its angles.
C) Using a compass and straightedge, copy an angle that appears to be close to 30°
from a diagram in your textbook.
D) Using a compass and straightedge, construct two parallel lines and label one of the
angles 30°.
6
7
21) In relation to constructions, a straightedge is
a) a clear plastic device devoid of markings.
B) often shaped like a triangle.
C) used for drawing straight lines or segments, but not for measuring.
D) all of the above.
22) One method of constructing an equilateral triangle is to simply construct a triangle
using the same segment for each side.
A) true
b) false
23) When constructing a line parallel to a given line, you will be
a) copying a segment.
B) bisecting a segment.
C) copying an angle
d) constructing a perpendicular
24) When constructing the bisector of a line segment, you are also constructing the
perpendicular bisector of the segment.
A)True
b)False
25) Name an angle supplementary to
a)  BOC
b)  BOE
c) DOC
d) BOA
26) Sara is making a shape with a piece of fabric. One corner is cut at an angle of 29
degrees. The angle at the opposite corner forms the complementary angle. What is the
measure of the angle in the opposite corner?
A. 29°
B. 58°
* C. 61°
D. 151°
7
8
27) The minute hand on a clock points directly at 12. The hour hand points directly at 4.
What is the measure of the smallest arc determined by the 2 hands?
28) A. 60°
* B. 120°
C. 150°
D. 240°
29) In the figure below, lines BE, CG, and AD, as well as ray HF, intersect at point H.
Which pair of angles must be congruent
*a)  CHD and  AHG
b)  CHD and  EHD
c)  BHC and  GHF
d)  FHE and  EHG
30) Which set of angle measures total 360 degrees?
* A. two pairs of supplementary angles
B. two pairs of complementary angles
C. one pair of complementary angles and one pair of supplementary angles
D. one pair of complementary angles, one pair of linear angles, and one pair of
supplementary angles
8
9
31) Which diagram below shows a correct mathematical construction using only a
compass and a straightedge to bisect an angle?
A)
b)
c)
d)
32) The measures of 2 angles are 46 0 and 440 . These are examples of which type of
angles?
A. vertical angles
B. a linear pair
C. supplementary angles
* D. complementary angles
33) Angle A and angle B are a linear pair. Angle A has a measure of 360 . What is the
measure of angle B? a) 36
b) 54
c) 144
d) 324
34) Given line PM, the drawing shows the beginning steps of a geometric construction.
Which construction is shown?
A. The perpendicular bisector of line PM.
* B. A line perpendicular to line PM at point P.
C. A line perpendicular to line PM at point M.
D. A line parallel to line PM through point P.
9
10
35) Which construction is shown in the accompanying diagram?
A) the bisector of  ACD
c) the perpendicular bisector of AB
b) the midpoint of DF
d) a perpendicular line to AB from point D
36)  DFG and  JKL are complementary angles. m  DFG  x  5 and m  JKL  x  9 m.
Find the measure of each angle.
a)
= 47,
c) DFG = 52,
= 53
= 48
b)
= 47,
= 43
d)
= 52,
= 38
37) In the figure shown, m  AED  1200 . Which of the following statements is false?
Not drawn to scale
a) m  AEB  600
C) m  BEC  1200
b)  BEC and  CED are adjacent angles.
d)  AED and  BEC are adjacent angles.
10
11
38) Use the figure below to answer question 4.
A pole sits on level ground. The pole is leaning 7° to the left of vertical, as shown in
the drawing. What is the measure of  1 ?
* A. 83°
B. 93°
C. 97°
D. 107°
39) Which geometric terms correctly describe the given triangle?
a)equilateral and equiangular
*b) Scalene and right
c)Isosceles and obtuse
d)Isosceles and acute
35) Which figure cannot be drawn?
a) an obtuse scalene triangle
*b) an obtuse equilateral triangle
c) an acute scalene triangle
d) an acute equilateral triangle
40) What is the measure of angle DCE?
a) 40
b) 50
*c) 70
d) 140
11
12
41) Identify the protractor that shows the measure of  XYZ as 60
a)
0
b)
c)
d)
42) In triangle ABC shown below, m  A  600 and m  C  800 . The exterior angle at B
measures x  100 . What is the value of x?
a) 30
b) 50
*c) 130
d) 140
43) m  DFG  2 x  6  and m  EFG  3x  11 . Find the value of x
0
0
a)35
b)37
c)39
d)41
12
13
44) What is x in the figure below?
A. 40 0
B. 700
C. 1100
* D. 1400
45) Find the values of x and y.
4y°
112°
7x + 7°
Drawing not to scale
a) x = 15, y = 17
b) = 112, y = 68
c) x = 68, y = 112
d) = 17, y = 15
0
46) m  3  37 Find m  1
1
4
2
3
Drawing not to scale
a) 37
b) 143
c) 27
d) 153
13
14
47) Find the value of x.
(7x – 8)°
(6x + 11)°
Drawing not to scale
a) -19
b) 125
48)
a) 4
c) 19
d) 55
In the figure below, CE is an angle bisector. What is the value of x
b)8
c)13
d)25
49) What is the measure of  CDE below
A. 2°
B. 40°
C. 50°
* D. 80
14
15
50) In which figure is point P on a perpendicular bisector of the triangle?
a)
c)
b)
d)
51) Which construction represents the center of a circle that is inscribed in a triangle?
A. The intersection of the three altitudes of the triangle.
B. The intersection of the three medians of the triangle.
*C. The intersection of the angle bisectors of each angle of the triangle.
D. The intersection of the perpendicular bisectors of each side of the triangle.
52) When proving that a triangle is a right triangle using coordinate geometry methods,
you must:
a) show that the slopes of two of the sides are negative reciprocals creating perpendicular
lines and right angles.
b) show that the lengths of the sides satisfy the Pythagorean Theorem, thus creating a
right
c) both choices 1 and 2 may be used.
d) neither choice 1 nor 2 may be used
53) When proving that a quadrilateral is a parallelogram by using slopes, you must find:
a) the slopes of all four sides
b) the slopes of two opposite sides.
c) the lengths of all four sides.
d) both the lengths and slopes of all four sides.
15
16
54) Which construction represents the center of a circle that is inscribed in a triangle?
A. The intersection of the three altitudes of the triangle.
B. The intersection of the three medians of the triangle.
* C. The intersection of the angle bisectors of each angle of the triangle.
D. The intersection of the perpendicular bisectors of each side of the triangle.
55) When given a square, the construction of an angle bisector at any vertex will create the
diagonal of the square.
A)True
b) false
56) 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?
A) on the triangle
b) outside the triangle
c) inside the triangle
d) the location varies
57) 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?
a) 8
b) 12
c) 16
d) 24
58) The point where the medians of a triangle are concurrent is called the
a) centroid
b) orthocenter
c) incenter
d) circumcenter
59) 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?
A) scalene
b) isosceles
c) equilateral
d)right
60) The orthocenter of a triangle is always located inside the triangle. A) true
b) false
16
17
61) 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.
A)16
b)18
c)24
d)36
62) The point of concurrence of the perpendicular bisectors of a triangle is always located
inside the triangle.
A) true
b) false
63) The point of concurrence of the angle bisectors of a triangle is always located inside
the triangle.
A) true
b) false
64) The centroid of a triangle divides the medians into ratios of
a) 2:1
b) 3:1
c) 4:1
d) 5:1
65) Regarding the diagram below, which of the following statements is TRUE?
a) Planes l and q are parallel planes.
c) Point P is in plane l.
b) Planes l and q intersect in line
d) None of the statements are true.
66) Line BH is parallel to plane P in the figure below. What is their intersection?
A. point A
B. point B
C. line BH
* D. There is no intersection.
17
18
67) What are three names for the angle?
L
1
N
M
68) BCR : Find the measures of  PMN and  NMR if MN bisects  PMR . The measure of
 PMR is 1360 .Draw a sketch that shows the given information. Explain your answer.
69) BCR : If
is opposite
and
is opposite
, what can you conclude? Explain.
70) BCR: Look at the figure below:
What is the value of x?
71) BCR: Look at the figure below:
What is the measure, in degrees, of  ACD ?
18
19
72) BCR: Look at the figure below:
What is the value of x ?
73) BCR: Look at the figure below: AB and DE intersect at point C
.
What is the measure, in degrees, of angle ACD?
74) BCR: Highlands Park is located between two parallel streets, Walker Street and James
Avenue. The park faces Walker Street and is bordered by two brick walls that
intersect James Avenue at point C, as shown below.
What is the measure, in degrees, of  ACB , the angle formed by the park’s two bricks
19
20
75) BCR: In the figure below, BD and AF intersect at point C.
In the figure below, BD and AF intersect at point
C.
20