Name _________________________________________
Geometry – Pd __
Date ____________
Constructions
Constructions
1. Congruent Line Segments
Given: (Line segment) AB
Task: To construct a line segment congruent to (line segment) AB
1. If a reference line does not already exist, draw a reference line with your
straightedge. Place a starting point on the reference line.
2. Place the point of the compass on point A.
3. Stretch the compass so that the pencil is exactly on B.
4. Without changing the span of the compass, place the compass point on the starting point on the
reference line and swing the pencil so that it crosses the reference line. Label your copy.
Your copy and (line segment) AB are congruent. Congruent means equal in length.
Example 1)
Example 2)
2. Congruent Angles
Given:
Regents
Common Core
BAC
Task: To construct an angle congruent to
BAC
1. If a reference line does not already exist, draw
a reference line with your straightedge. Place
a starting point on the reference line.
2. Place the point of the compass on the vertex
of BAC (point A).
3. Stretch the compass to any length so long as it stays ON the angle.
4. Swing an arc with the pencil that crosses both sides of BAC .
5. Without changing the span of the compass, place the compass point on the starting point of the
reference line and swing an arc that will intersect the reference line and go above the reference line.
6. Go back to BAC and measure the width (span) of the arc from where it crosses one side of the
angle to where it crosses the other side of the angle.
7. With this width, place the compass point on the reference line where your new arc crosses the
reference line and mark off this width on your new arc.
8. Connect this new intersection point to the starting point on the reference line.
Example 1)
Example 2)
3. Construct an Angle Bisector
Given:
Regents
Common Core
BAC
Task: Bisect
BAC
1. Place the point of the compass on the vertex
of BAC (point A).
2. Stretch the compass to any length so long as
it stays ON the angle.
3. Swing an arc so the pencil crosses both sides of BAC . This will create two intersection points
with the sides (rays) of the angle.
4. Place the compass point on one of these new intersection points on the sides of BAC . If needed,
stretch your compass to a sufficient length to place your pencil more than halfway into the interior of
the angle.
Stay between the sides (rays) of the angle. Place an arc in this interior - you do not need to cross the
sides of the angle.
5. Without changing the width of the compass, place the point of the compass on the other intersection
point on the side of the angle and make the same arc. Your two small arcs in the interior of the angle
should be crossing.
6. Connect the point where the two small arcs cross to the vertex A of the angle.
Example 1)
Example 2)
Name _________________________________________
Geometry – Pd __
Date ____________
Constructions
Constructions HW
̅̅̅̅, construct a congruent segment.
1) Using 𝐴𝐵
[Leave all construction marks]
2) Construct an angle congruent to < 𝐴𝐵𝐶
[Leave all construction marks]
3) Create an angle bisector for < 𝑀𝐽𝐻.
[Leave all construction marks]
4) Using a compass, construct the bisector
of < ABC. [Leave all construction marks]
_____5) When given a square, the construction of an angle bisector at any vertex will create the
diagonal of the square.
(1) True
(2) False
_____ 6) Which illustration shows the correct construction of an angle bisector?
(1)
(2)
(3)
(4)
_____ 7) Based on the construction to the right, which statement must be true?
1
(1) 𝑚 < 𝐴𝐵𝐷 = 𝑚 < 𝐶𝐵𝐷
2
(2) 𝑚 < 𝐴𝐵𝐷 = 𝑚 < 𝐶𝐵𝐷
(3) 𝑚 < 𝐴𝐵𝐷 = 𝑚 < 𝐴𝐵𝐶
1
(4) 𝑚 < 𝐶𝐵𝐷 = 2 𝑚 < 𝐴𝐵𝐷
_____ 8) As shown in the diagram, a compass is used to find points D and E,
equidistant from point A. Next the compass is used to find point F,
equidistant from point D and E. Finally, a straight edge is used to
draw AF. Which statement must be true?
̅̅̅̅ bisects side 𝐵𝐶
̅̅̅̅
(1) 𝐴𝐹
̅̅̅̅
(2) 𝐴𝐹 bisects < 𝐵𝐴𝐶
̅̅̅̅ ⊥ 𝐵𝐶
̅̅̅̅
(3) 𝐴𝐹
(4) ∆ ABG ~∆ ACG
_____ 9) The diagram shows the construction of the bisector of < 𝐴𝐵𝐶.
Which statement is not true?
1
(1) 𝑚 < 𝐸𝐵𝐹 = 𝑚 < 𝐴𝐵𝐶
2
1
(2) 𝑚 < 𝐷𝐵𝐹 = 𝑚 < 𝐴𝐵𝐶
2
(3) 𝑚 < 𝐸𝐵𝐹 = 𝑚 < 𝐴𝐵𝐶
(4) 𝑚 < 𝐷𝐵𝐹 = 𝑚 < 𝐸𝐵𝐹
_____ 10) A straight edge and compass were used to create the following construction.
Which statement is false?
(1) 𝑚 < 𝐴𝐵𝐷 = 𝑚 < 𝐷𝐵𝐶
1
(2) (𝑚 < 𝐴𝐵𝐶) = 𝑚 < 𝐴𝐵𝐷
2
(3) 2(𝑚 < 𝐷𝐵𝐶) = 𝑚 < 𝐴𝐵𝐶
(4) 2(𝑚 < 𝐴𝐵𝐶) = 𝑚 < 𝐶𝐵𝐷
Review Section!!
_____ 11) In the diagram, transversal TU intersects PQ and RS at V and W respectively.
If m<TVQ = 5x – 22 and m<VWS = 3x + 10, for which value of x is PQ//RS?
(1) 6
(2) 16
(3) 24
(4) 28
_____ 12) When the system of equations 𝑦 + 2𝑥 = 𝑥 2 and 𝑦 = 𝑥 is graphed on a
set of axes, what is the total number of points of intersection?
(1) 0
(2) 1
(3) 2
(4) 3
_____ 13) The equation of a line is 3𝑦 + 2𝑥 = 12. What is the slope of the line
perpendicular to the given line?
3
2
(1)
(2)
2
(3)
3
−2
3
2
(4) − 3
Constructions HW Answers
1)
2)
3)
4)
5) (1)
6) (3)
7) (2)
8) (2)
9) (3)
10) (4)
11) (2)
12) (3)
13) (1)
Review Section!!
11) In the diagram, transversal TU intersects PQ and RS at V and W respectively.
If m<TVQ = 5x – 22 and m<VWS = 3x + 10, for which value of x is PQ//RS?
12) When the system of equations 𝑦 + 2𝑥 = 𝑥 2 and 𝑦 = 𝑥 is graphed on a
set of axes, what is the total number of points of intersection?
13) The equation of a line is 3𝑦 + 2𝑥 = 12. What is the slope of the line
perpendicular to the given line?