Name ________________________
Worksheet 3.8
Practice Exercises for Unit 3 Test
1. As we have talked about last unit, a bi-conditional statement is a statement that is true “both
ways”. The wording “p if and only if q”, abbreviated as “p iff q”, is the most common way to
denote such a relationship.
Indicate if the following logical statements are True or False. Recall that true statements
must always be true. Provide a clear counter-example if the statement is False – a wellannotated diagram suffices.
___ A quadrilateral is a kite iff it has exactly one pair of congruent, opposite angles.
___ Congruent triangles  SSA.
___ The quad. has  diagonals  the quadrilateral is a rhombus.
___ Congruent quads iff SSSSA.
___ The statement is a definition iff the statement is bi-conditional.
2. Polygons
a. There exists only one regular polygon with an interior angle whose measure is exactly
three times the measure of its exterior angle. Name the polygon.
b. PENTA is a regular pentagon. Select a vertex and argue why the two diagonals
constructed from this vertex trisect an angle of the pentagon.
c. PQRS is a square. What are the coordinates of R and S?
3. The Mid-Segment Theorem
The segment joining the midpoints of two sides of an arbitrary triangle (called the “midsegment”) is parallel to the third side and half its length.
a. Prove the Mid-Segment Theorem using coordinate methods.
b. Prove using a proof method of your choice.
Given: Quadrilateral ABCD with
D
midpoints W, X, Y, and Z as
Z
W
shown in the diagram.
C
A
Y
X
Prove: WXYZ is a parallelogram
B
4. Complete the following proof:
C
Given: D is a midpoint of AC
E is a midpoint of CB
DE  EF
Prove: ABFD is a parallelogram
D
E
F
A
B
Statements
Reasons
5. Complete the following prooft:
Given:
ABCD is a parallelogram
DE  AB
BG  AD
DE  BG
Prove:
CDFB is a kite