# Unit 4 - Lakeside School ```Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
Name: __________________________
Wed. 11/6 or Thu. 11/7 2013
Unit 4 Test
Honors Geometry 2013-2014
Instructions
 Each question is weighted equally
 Read instructions to each problem carefully
 Manage your time to make sure you get something down for every part of every
problem


Calculators are OK
Use the provided “Tools list” as needed
Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
1. Multiple Choice
Choose all correct options. You might need to select none, some, or all of the options.
a. Which of the following statements are TRUE?

If a quadrilateral is not a square, then it does not have perpendicular diagonals.

If two angles of a trapezoid have been shown to be congruent, then the trapezoid is isosceles.

If a quadrilateral has diagonals that are perpendicular but not congruent, then it is a kite.

If the diagonals of a quadrilateral are perpendicular and congruent, then it is a square.
b. In quadrilateral ABCD, diagonal BD bisects ABC and side AB is NOT congruent to
side CD . ABCD could be which of the following?

kite

parallelogram

rectangle

trapezoid

isosceles trapezoid
c. Which of the following could be used as minimum conditions to establish the congruence

SASAS

SSSAA

SSSSA

Two quadrilaterals are parallelograms and they have been shown to have one congruent
diagonal.

Two quadrilaterals are isosceles trapezoids and they have been shown to have one congruent
diagonal.
Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
2.
a. Prove the following : If the diagonals of a parallelogram are , then the parallelogram
is a rhombus.
T
S
Given: QRST is a
and RT  SQ
Prove: QRST is a rhombus
R
Statements
Reasons
Q
Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
b. Complete the proof
B
C
Given: AB  DC , AB  BC and DC  BC :
Prove:
E
DEC is isosceles
A
Statements
Reasons
D
Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
3. Polygons and angles
Given a regular octagon ABCDEFG, and two equilateral triangles FGX and DEY. Answer
the following questions. No work need be shown, but it can help you get partial credit. You
A
a. What is the measure of ABC?
B
H
b. What is the measure of BAC?
C
G
X
D
F
E
c. Find ∠𝐷𝑍𝐸 (where point 𝑍 is at the intersection of ⃡𝐸𝐹 and ̅̅̅̅
𝐷𝑌.
d. If you continued adding sides of equal length at equal angles from the vertices X, F, E,
and Y, you would construct a gigantic regular polygon below the figure. How many sides
would this polygon have?
Z
Y
Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
4. The mid-segment theorem
a. Prove the mid-segment theorem:
Each mid-segment (segment connecting the midpoints of two sides) of a triangle is
parallel to and half the length of the third side.
Unit 4 Test – Quadrilaterals and Polygons
Honors Geometry 2013-2014
5. The mid-segment parallelogram
You were shown the following surprising result during class. Now prove it is true!
The figure formed by connecting the midpoints of adjacent sides of any quadrilateral is
a parallelogram.
Hints – You need to construct a diagonal and you need to use the mid-segment theorem from question 4.
You need not have completed the proof of the mid-segment theorem to do this proof. Just use the result.
D
Z
Given: Quadrilateral ABCD with midpoints W, X,
W
Y, and Z as shown in the diagram.
C
A
Prove: WXYZ is a parallelogram
Y
X
B
Statements
Reasons
```