Download If the diagonal divides the quadrilateral into two congruent triangles

Name: ______________________________________
Date :________________
424 First Test Third Quarter
Show all work for full credit, partial credit may be awarded for correctly shown work.
1. Complete each statement with always (A), sometimes 2. Find the measure of x and y in the accompanying
(S), or never (N) to make the statement true.
diagram given the quadrilateral is a square.
a. If the diagonal divides the quadrilateral
into two congruent triangles, then the
quadrilateral is _______ a parallelogram.
b. If MX  NX , then X ____ lies on the
x y
perpendicular bisector of MN .
c. In EFGH, EF is ______ congruent
to GH .
d . The sum of the measures of the angles of a
polygon formed by joining consecutive
midpoints of a polygon's sides is _______
equal to the sum of the measures of the
angles of the original polygon.

e. A rhombus with no right angles _______ has
congruent diagonals.
3. Find the measure of x and y in the accompanying
diagram given the quadrilateral is a rhombus.
4. Find the value(s) of x in the accompanying diagram.
27
65
16
x
y
x2 - 6x
5. B and H are the midpoints of AC and AG respectively, C and G are the midpoints
of BD and HE respectively. If BH  x  y  6, FG  2 x  y, CF  3 y  7 x  4, and
A
DE  22. Find the value of x and y.
H
B
G
C
F
E
D
6. Find the values of x in the figure below.
64
9x - 8
x2
7a. Which is longer in the figure below EC or AE ?
B
C
55
50
80
7b. Which is the shortest segment?
27
D
70
E
33
40
A
Figure not drawn to scale
A
8. Given: ABC with AB  AC ,
BE and DE are the bisectors of ABC and ADB respectively
Prove: BE  DE
E
B
Statement
Reason
D
C
9. Given: ABCD is a parallelogram, AJ  CE
Prove: GH  FG
Statement
Reason
Choose the most appropriate answer choice for each question below. Write the numerical choice in the s pace
provided next to each question. No partial credit is awarded in this section.
1. In the accompanying figure, WXYZ is a rectangle. which one of the following
W
X
2
3
is false?
1 XYZ  YXW
 3 WOX  ZOY
 2  2 is complementary to 3  4 3  WOX
 5 Cannot be determined by the information given.
1
O
Y
Z
2. A is greater than its complement, and the complement of A is greater than  B.
Which of the following must be true?
1 B is greater than A.
 2  Complement of A is greater than complement of B.
 3 B is greater than the complement of B.
 4  Complement of B is greater than complement of A.
 5 Cannot be determined by the information given.
N
M
3. In the accompanying figure, which one of the following would not allow you
to prove that quadrilateral LMNO is a parallelogram?
1 MP  PO and LP  PN
L
 2  LO  MN and MLP is supplementary to LMN .
 3 MLO is supplementary to LON and LON is supplementary to ONM .
 4  1  2, and MNL  LNO.
4. Which one of the following can be proved true?
I. The medians of a triangle are congruent
II. Corresponding medians of congruent triangles are congruent.
III. A median of a triangle is also an angle bisector.
1 I only
 4  I, II, III
 2 II only
 3 II and III only
5  None of the above
2 1
3
P
0