This is Just a Test!

This is Just a
Test!
Unit 01c: Constructions, Other Stuff
(SB PAP Geometry) Extra Problems
Name:
Block:
1.
Using only your compass and straightedge, construct a pair of parallel lines such that ∠1 and ∠2 are Same-Side Interior
angles and such that ∠1 ≅ ∠𝐴, as shown below.
A
a) Use ∠𝐴 above to construct a pair of parallel lines such that ∠𝐴 is one of a pair of alternate interior angles.
b) Use ∠1 below to construct a pair of parallel lines such that ∠1 and ∠2 (not shown) are a pair of Same-Side Interior
Angles. To receive full credit, you must construct both angles 1 and 2 in the proper positions.
1
2.
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ , as shown below.
Use a compass and straightedge to construct square 𝑆𝑄𝑅𝐸 such that 𝑆𝑄
C
a)
D
̅̅̅̅ ≅ 𝐴𝐵
̅̅̅̅ , as shown below.
Use a compass and straightedge to construct square 𝑆𝑄𝑅𝐸 such that 𝑆𝑄
A
B
b) Use a compass and straightedge to construct rectangle 𝑅𝐸𝐶𝑇 such that ̅̅̅̅
𝑅𝐸 ≅ ̅̅̅̅
𝐴𝐵, as shown above, and ̅̅̅̅
𝐸𝐶 ≅ ̅̅̅̅
𝐸𝐹 , as
shown below.
E
F
3.
⃗⃗⃗⃗⃗ is an angle bisector,
Given that mRAN = 88° and 𝐴𝐷
find the value of x.
5.
A
R
Complete the diagram to demonstrate that the Lines
Perpendicular to a Transversal Theorem is invalid in
Elliptic geometry.
N
D
2
(2x + 3x)°
a)
Find the value of 𝑥 if ⃗⃗⃗⃗⃗⃗⃗
𝑅𝑊 bisects ∠𝑆𝑅𝑇. Then find
the measures of each angle.
a)
S
(6x2 - 1)°
Complete the diagram to demonstrate that the
Perpendicular Transversal Theorem is invalid in
Elliptic geometry.
b) Complete the diagram to demonstrate that the
Euclidean theorem Perpendicular lines intersect to
form 4 right angles needs to be amended for Elliptic
geometry.
W
(34 - x)°
R
T
⃗⃗⃗⃗⃗⃗ bisects ABC. Find mABC.
b) In the diagram, 𝐵𝐷
6.
Find the equation of the perpendicular bisector of the
segment with endpoints at (3, −7) and (6, 2). Write your
answer in point-slope form.
a)
4.
In the diagram, 𝑚 ∥ 𝑛. Find the value of 𝑥.
m
42
x
124
a)
n
In the diagram, 𝑚 ∥ 𝑛. Find the value of 𝑥.
24°
x
149°
b) In the diagram, 𝑚 ∥ 𝑛. Find the value of 𝑥.
27°
36°
x
153°
Find the equation of the perpendicular bisector of
the segment with endpoints at (-5, 2) and (2, -1).
Write your answer in point-slope form.
b) Find the equation of the perpendicular bisector of
the segment with endpoints at (0, 3) and (4, -7).
Write your answer in point-slope form.
7.
Kenny attempted to prove the Symmetric Property of Angle Congruence, but he made a fatal mistake. Explain what is
wrong with Kenny’s “proof.”
K
Given: ∠𝐾 ≅ ∠𝑌
Prove: ∠𝑌 ≅ ∠𝐾
Statements
1. ∠𝐾 ≅ ∠𝑌
Reasons
1. Given
2. ∠𝑌 ≅ ∠𝐾
2. Symmetric Property of  Angles
a) Explain why you cannot use a given theorem to prove that theorem.
b) Correct the above proof.
Y