E Test: Unit 2c Constructions! Block: Name:

Test: Unit 2c Constructions!
Block:
Name:
E
1.
Use a compass and a straightedge together with ∠𝐸 above to construct one of the following.
a) Given ∠𝐸 is the vertex angle of isosceles ∆𝑍𝐸𝑃, construct ∠𝑍.
b) Given ∠𝐸 and ∠𝑇 are base angles of isosceles ∆𝐵𝐸𝑇, construct ∠𝐵.
a) Complete part a) or b) above, whichever you did not do on the test.
b) Construct two different, non-similar isosceles triangles ∆𝑅𝑂𝑊 using ∠𝑅 below.
R
2.
Recall that the Euler Line contains the orthocenter, the centroid, and the circumcenter of a triangle. Construct the Euler
Line for the triangle below, labeling the exact location of the appropriate points of concurrency.
a)
Construct the Euler Line for the triangle below, labeling the exact location of the appropriate points of concurrency.
b) Construct the Euler Line for the triangle below, labeling the exact location of the appropriate points of concurrency.
3.
For the 3 people who do not know, the Deathly Hallows represents the Invisibility
Cloak (equilateral triangle), the Resurrection Stone (circle), and the Elder Wand
(vertical segment) as bestowed upon the three Peverell brothers by Death.
Construct the Deathly Hallows using ̅̅̅̅
𝐻𝑃 (shown below) as one of the sides of the
Invisibility Cloak. Then give the geometric name for each of the following:
Resurrection Stone: _________________________
Elder Wand: _______________________________
H
a)
P
Construct the Deathly Hallows using the circle below as the circle representing the Resurrection Stone.
R
b) Construct the Deathly Hallows using EW below as the segment representing the Elder Wand.
E
W
4.
3
̅̅̅̅ below, construct the smallest possible segment 𝑅𝑆
̅̅̅̅ and the largest possible segment 𝑃𝑄
̅̅̅̅
In Δ𝐴𝐵𝐶, 𝐵𝐶 = 4 𝐴𝐵. Using 𝐴𝐵
̅̅̅̅ is the third side of Δ𝐴𝐵𝐶.
such that 𝑅𝑆 < 𝐴𝐶 < 𝑃𝑄, where 𝐴𝐶
A
a)
B
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ , construct the largest possible
Using 𝐴𝐵
̅̅̅̅
segment 𝑅𝑆 and the smallest possible segment ̅̅̅̅
𝑃𝑄
̅̅̅̅ is the third side
such that 𝑅𝑆 < 𝐴𝐶 < 𝑃𝑄, where 𝐴𝐶
of Δ𝐴𝐵𝐶.
B
A
B
C
3
̅̅̅̅ below, construct the largest possible segment 𝑅𝑆
̅̅̅̅ and the smallest possible segment
b) In Δ𝐴𝐵𝐶, 𝐵𝐶 = 2 𝐴𝐵. Using 𝐴𝐵
̅̅̅̅
̅̅̅̅
𝑃𝑄 such that 𝑅𝑆 < 𝐴𝐶 < 𝑃𝑄, where 𝐴𝐶 is the third side of Δ𝐴𝐵𝐶.
A
B