Name _________________________
Parallel Lines and Properties of Quadrilaterals
Parallel Lines Cut by a Transversal: parallel lines a and b are cut by transversal l
a
b
2
1
3
4
5
6
8
7
l
Vertical Angles: congruent (example: 2 & 3) Can you list more vertical pairs?
Corresponding Angles: congruent (example: 1 & 5) Can you list more corresponding pairs?
Alternate Interior Angles: congruent (example: 3 & 6) Can you list another AIA pair?
Alternate Exterior Angles: congruent (example: 1 & 8) Can you list another AEA pair?
Same Side Interior Angles: supplementary or adds up to 180 degrees (example: 3 & 5) Can you list
another SSI pair?
Same Side Exterior Angles: supplementary (example: 1 & 7) Can you list another SSE pair?
Ex. 1 In the trapezoid below, AB is parallel to DC . What is the measure of < C ?
Ex. 2 In the figure below, B is on DE and DE ║ AC . Which of the following angle congruences must
hold?
F.  1   2
G.  1   4
H.  2   3
J.
2  4
K.  3   4

Ex. 3 In the figure below, ABCD is a trapezoid, E lies on AD , and angle measures are as marked. What
is the measure of <BDC?
Ex. 4 In the figure below, lines m and n are parallel, transversals r and s intersect to form an angle of
measure x°, and 2 other angle measures are as marked. What is the value of x?
A. 15
B. 25
C. 35
D. 65
E. 80
Ex. 5 In the figure below, B is on AC , E is on DF , AC is parallel to DF , and BE is congruent to
BF . What is the measure of <DEB ?
Ex. 6 In the figure below, A, C, F, and D are collinear; B, C, and E are collinear; and the angles at A, E,
and F are right angles, as marked. Which of the following statements is NOT justifiable from the given
information?


F. AB is parallel to EF .
G. DE is perpendicular to BE .
H. <ACB is congruent to <FCE.
J. ΔABC is similar to ΔEFC.
K. CE is congruent to ED .
Ex. 7 In the figure below, transversal r crosses both p and q, and a° and b° are measures of the indicated
angles, both between 0° and 180°. Lines p and q will cross somewhere to the left of transversal r (that is,
on the side opposite the indicated angles). Which of the following statements best expresses a true
relationship between a and b for all possible positions of transversal r?
F. a < b
G. a = b
H. a + b < 180
J. a + b= 180
K. a + b> 180
Properties of Various Quadrilaterals
Sum of the interior angles of ANY quadrilateral: 360°
Ex. 8 Find the measure of angle C:
118°
99°
27°
C
Diagonals of a Rectangle: bisectors
Diagonals of a Square or a Rhombus: perpendicular bisectors
Diagonals of a Kite: perpendicular
Mark all congruent sides and angles in the above shapes
Ex. 9 Rectangle ABCD, with diagonals AC and BD intersecting at point E, is shown below. Rectangle
ABCD is a square if and only if ΔABE is congruent to which of the triangles in the following list?
A. ΔACD
B. ΔADE
C. ΔBAE
D. ΔBDC
E. ΔCDE
Ex. 10 In rhombus ABCD shown below, diagonal AC is 8 inches long, and diagonal BD is 6 inches long.
What is the perimeter of the rhombus?
A
B
D
C
Ex. 11 In the figure below, ABCD is a rectangle. If the diagonal AC is 13 inches long and BC is 5 inches
long, what is the area of the rectangle?
A
B
D
C
Name _________________________
Parallel Lines and Properties of Quadrilaterals Practice A
A
B
1. The figure below shows quadrilateral ABCD. What is the measure of <C?
43
2. What is the value of x?
41
(4x) °
71
C
D
(x + 36)°
3. In the figure below, AB is parallel to CD. What is the value of x + y ?
B
A
30°
55°
x°
C
y°
D
4. In the figure below line a is parallel to line b, and they are both intersected with transversals t and m.
Find the value of x.
a
80°
b
25°
x°
m
t
5. In the figure below, parallel lines a and b are cut by transversal t. Find the value of y.
a
104°
(x+2y)°
(2x)°
t
b
118°
6. Find the measure of angle C. SHOW WORK!
(5x)°
C
(2x+12) °
90°
118°
99°
27°
C
118°
99°
27°
C
7. For the figure below, AE  EC , AD  AB and AED measures 90 °. Which of the following must
be true?
I. ABCD is a rectangle
II. ABCD is a square
III. ABCD is a rhombus
A. I only
B. II and III
C. I and II
D. II only
E. III only
8. In the figure below, ABCD is a rectangle. If the diagonal AC is 25 inches long and BC is7 inches
long, what is the area of the rectangle? SHOW WORK!
WORK:
A
B
D
C
9. In rhombus ABCD shown below, diagonal AC is 24 inches long, and diagonal BD is 10 inches long.
What is the perimeter of the rhombus? SHOW WORK!
A
B
WORK:
D
C
Name _________________________
Parallel Lines and Properties of Quadrilaterals Practice B
1. The figure below shows quadrilateral ABCD. What is the measure of <C?
F. 120°
G. 115°
H. 105°
J. 100°
K. 80°
2. What is the value of x?
(4x) °
84°
3. In the figure, AB is parallel to CD. What is the value of x?
B
A
40°
45°
C
x°
D
4. In the figure below line a is parallel to line b, and they are both intersected with transversal t. Find the
value of x.
a
82°
b
x°
t
a
5. In the figure below, parallel lines a and b are cut by transversal t.
Find the value of x.
b
104°
(2x)°
6. Find the value of x. SHOW WORK!
t
121°
(2x)°
(x)°
89°
118°
99°
27°
C
7. AED is a right angle. Can we say that the figure below is a square with the given information? Why
or why not?
118°
99°
27°
C
A
E
D
8. In the figure below, ABCD is a rectangle. If the diagonal AC is 15 inches long and BC is 9 inches
long, what is the length of AB? SHOW WORK!
A
B
D
C
WORK:
9. In rhombus ABCD shown below, diagonal AC is 24 inches long, and diagonal BD is 10 inches long.
What is the length of AD? SHOW WORK!
WORK:
A
B
D
C