Name _________________________________________
Geometry – Pd __
Date ____________
Constructions
Constructions Day 2
1. Construct an Equilateral Triangle
Regents
Common Core
Given: (Line segment) AB
Task: To construct an equilateral triangle
1. Place the point of the compass on point A and
measure (place the pencil) to point B. Swing a
large arc up above the given line.
2. Place the point of the compass on point B and
measure (place the pencil) to point A. Swing a large arc up above the given line.
3. Create the missing two sides of the equilateral triangle by connecting point A to the point of
intersection, and then point B to the point of intersection.
Example 1)
Example 2)
Common Core Application:
1) Margie has three cats. She has heard that cats in a room position themselves at equal distances from
one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of
her bed (at S), while JoJo, her Siamese, is laying on her desk chair (at J). If the theory is true, where will
she find Mack, her calico cat? Use the scale drawing of Margie’s room shown below, together with
(only) a compass and straightedge. Place an M where Mack will be if the theory is true.
2. Construct a 𝟑𝟎° Angle
Regents
Common Core
Given: (Line segment) AB
Task: To construct a 30° Angle
1. First, construct an equilateral triangle
based on segment ̅̅̅̅
𝐴𝐵.
a) Place the point of the compass on point A and measure
to point B. Swing a large arc up above the given line.
b) Place the point of the compass on point B and measure to point A. Swing a large arc up
above the given line.
c) Create the missing two sides of the equilateral triangle by connecting both point A and point B
to the point of intersection
2. Second, bisect any angle of the equilateral triangle.
a) Place the point of the compass on the vertex
b) Stretch the compass to any length so long as it stays ON the angle
c) Swing an arc so the pencil crosses both sides of the angle
d) Place the compass point on one of these new intersection points on the sides of the angle and
swing an arc (using the pencil) on the interior of the angle.
e) Without changing the width of the compass, complete the same for the other point of intersection.
f) Connect the point where the two small arcs cross to the vertex of the angle.
3. You have now created the construction of a 30° angle.
Name _________________________________________
Geometry – Pd __
Date ____________
Constructions
Constructions Day 2 HW
̅̅̅̅, construct an equilateral triangle.
1) Using 𝐴𝐵
[Leave all construction marks]
2) Construct an angle bisector to < 𝑀𝐽𝐻
[Leave all construction marks]
3) ∆ 𝐴𝐵𝐶 is shown below. Is it an equilateral
triangle? Justify your response.
4) Using equilateral ∆ 𝐴𝐵𝐶 to construct a 30°
angle. [Leave all construction marks]
_____ 5) One method of constructing an equilateral triangle is to simply construct a triangle using the
same segment for each side.
(1) True
(2) False
_____ 6) Which diagram shows the construction of a 30° angle?
_____ 7) The diagram shows the construction of an equilateral triangle.
Which statement justifies this construction?
(1) < 𝐴 + < 𝐵 + < 𝐶 = 180
(2) < 𝐴 = < 𝐵 = < 𝐶
(3) 𝐴𝐵 = 𝐵𝐶 = 𝐴𝐶
(4) 𝐴𝐵 + 𝐵𝐶 > 𝐴𝐶
_____ 8) The diagram below shows the construction of the bisector of ∡ 𝐴𝐵𝐶.
Which statement is not true?
1
1) 𝑚∡ 𝐸𝐵𝐹 = 2 𝑚∡ 𝐴𝐵𝐶
1
2) 𝑚∡ 𝐷𝐵𝐹 = 2 𝑚∡ 𝐴𝐵𝐶
3) 𝑚∡ 𝐸𝐵𝐹 = 𝑚∡ 𝐴𝐵𝐶
4) 𝑚∡ 𝐷𝐵𝐹 = 𝑚∡ 𝐸𝐵𝐹
Review Section!!
_____ 9) What is the equation of a line passing through the point (4, −1) and parallel to the line whose
equation is 2𝑦 − 𝑥 = 8?
1
1
(1) 𝑦 = 2 𝑥 − 3
(2) 𝑦 = 2 𝑥 − 1
(3) 𝑦 = −2𝑥 + 7
(4) 𝑦 = −2𝑥 + 2
_____ 10) In the diagram of ∆𝑃𝑄𝑅 shown below, PR is extended to S,
m<P = 110, m<Q = 4x, and m<QRS = 𝑥 2 + 5𝑥. What is the m<Q?
(1) 44
(2) 40
(3) 11
(4) 10
_____ 11) The solution of the system of equations 𝑦 = 𝑥 2 − 2 and 𝑦 = 𝑥 is:
(1) (1,1) and (−2, −2)
(2) (2,2) and (−1, −1)
(3) (1,1) and (2,2)
(4) (−2, −2) and (−1, −1)
_____ 12) Lines p and q are intersected by line r, as shown. If m<1 = 7x – 36 and
m<2 = 5x + 12, for which value of x would p//q?
(1) 17
(2) 24
(3) 83
(4) 97
Constructions Day 2 HW
1)
2)
3)
4)
5) (1)
6) (1)
7) (3)
8) (3)
9) (1)
10) (2)
11) (2)
12) (1)
9) What is the equation of a line passing through the point (4, −1) and parallel to the line whose
equation is 2𝑦 − 𝑥 = 8?
10) In the diagram of ∆𝑃𝑄𝑅 shown below, PR is extended to S,
m<P = 110, m<Q = 4x, and m<QRS = 𝑥 2 + 5𝑥. What is the m<Q?
11) The solution of the system of equations 𝑦 = 𝑥 2 − 2 and 𝑦 = 𝑥 is:
12) Lines p and q are intersected by line r, as shown. If m<1 = 7x – 36 and
m<2 = 5x + 12, for which value of x would p//q?