Chapter
6
Chapter Review
6
Chapter Review
Vocabulary Review
Resources
base angles of a trapezoid (p. 336)
consecutive angles (p. 312)
isosceles trapezoid (p. 306)
kite (p. 306)
midsegment of a trapezoid (p. 348)
parallelogram (p. 306)
rectangle (p. 306)
rhombus (p. 306)
square (p. 306)
trapezoid (p. 306)
Student Edition
Extra Skills, Word Problems, Proof
Practice, Ch. 6, p. 726
English/Spanish Glossary, p. 779
Postulates and Theorems, p. 770
Table of Symbols, p. 763
To complete each definition, find the appropriate word in the second column.
1. A(n) 9 is a parallelogram with four right angles. F
A. parallelogram
2. A(n) 9 is a quadrilateral with two pairs of adjacent
sides congruent and no opposite sides congruent. H
B. trapezoid
3. Angles of a polygon that share a common side
are 9. G
D. base angles
4. A(n) 9 is a quadrilateral with exactly one pair of
parallel sides. B
E. isosceles trapezoid
5. A(n) 9 is a parallelogram with four congruent sides. I
G. consecutive angles
6. The 9 of a trapezoid is the segment that joins the
midpoints of the nonparallel opposite sides. J
H. kite
7. A(n) 9 is a quadrilateral with both pairs of
opposite sides parallel. A
Vocabulary and Study Skills
worksheet 6F
Spanish Vocabulary and Study
Skills worksheet 6F
Interactive Textbook Audio
Glossary
Online Vocabulary Quiz
C. square
F. rectangle
I. rhombus
J. midsegment
8. A(n) 9 is a parallelogram with four congruent sides
and four right angles. C
For: Vocabulary quiz
Web Code: auj-0651
9. A(n) 9 is a trapezoid whose nonparallel opposite sides are
congruent. E
10. Two angles that share a base of a trapezoid are
its 9. D
Skills and Concepts
Spanish Vocabulary/Study Skills
Vocabulary/Study Skills
Special quadrilaterals are defined by their characteristics.
6-1 Objective
To define and classify
special types of
quadrilaterals
Name
Class
6D: Vocabulary
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
A rhombus is a parallelogram with four congruent sides.
A rectangle is a parallelogram with four right angles.
A square is a parallelogram with four congruent sides and four right angles.
A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite
sides congruent.
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
An isosceles trapezoid is a trapezoid whose nonparallel opposite sides are congruent.
ELL
L3
Date
For use with Chapter Review
Study Skill: Always read direction lines before doing any exercises.
What you think you are supposed to do may be quite different than
what the directions call for.
Circle the word that best completes the sentence.
1. (Parallel lines, Perpendicular lines) are lines in the same plane that
never intersect.
2. The point where a line crosses the y-axis is known as the
(x-intercept, y-intercept).
3. The linear equation y = mx + b is in (slope-intercept, point-slope) form.
4. The (slope, equation) of a line is its rate of vertical change over
horizontal change.
5. Two lines are (parallel, perpendicular) if the product of their slopes is -1.
6. A (slope, translation) shifts a graph horizontally, vertically, or both.
7. The (domain, range) of a relation is the set of second coordinates in
the ordered pairs.
8. An equation that describes a function is known as a (function rule,
function notation).
9. (Dependent, Independent) events are events that do not influence
one another.
10. The (mean, median) is the middle value in a set of numbers when
arranged in numerical order.
11. A power has two parts, a (base, coefficient) and an exponent.
Draw and label each quadrilateral with the given vertices. Then determine the
most precise name for each quadrilateral. 11–12. See back of book.
11. N(-1, 2), M(3, 4), L(1, -2), K(5, 0)
© Pearson Education, Inc. All rights reserved.
PHSchool.com
12. A(n) (exponent, variable) is a symbol, usually a letter, that represents
one or more numbers.
13. The (absolute value, reciprocal) of a number is its multiplicative inverse.
14. The equation 3 + 4 = 4 + 3 illustrates the (Identity Property of Addition,
Commutative Property of Addition).
12. P(-4, 2), Q(-1, 3), R(7, 0), S(4, -1)
15. When a value is less than its original amount, the percent of (increase,
decrease) can be found.
16. The (complement of an event, experimental probability) consists of all
the outcomes not in the event.
17. A V-shaped graph that points upwards or downwards is the graph of
a(n) (linear, absolute value) equation.
18. Another name for a number pattern is a (conjecture, sequence).
Chapter 6 Chapter Review
357
24
Reading and Math Literacy Masters
Algebra 1
357
x 2 Algebra Find the values of the variables and the lengths of the sides.
13. isosceles trapezoid ABCD
14. kite KLMN
L
m3
A 2x 2 B
2x 7
x1
K
M
3m 5
t9
N
m ≠ 4, t ≠ 5; 7, 14, 14, 7
C
x1
x ≠ 8; 9, 14, 9, 7
D
6-2 and 6-3 Objectives
m 2t
Opposite sides and opposite angles of a parallelogram are congruent.
The diagonals of a parallelogram bisect each other.
To use relationships
among sides and among
angles of parallelograms
If three (or more) parallel lines cut off congruent segments on one transversal,
then they cut off congruent segments on every transversal.
To use relationships
involving diagonals of
parallelograms or
transversals
A quadrilateral is a parallelogram if any one of the following is true.
Both pairs of opposite sides are congruent.
Both pairs of opposite angles are congruent.
The diagonals bisect each other.
One pair of opposite sides is both congruent and parallel.
To determine whether a
quadrilateral is a
parallelogram
Find the measures of the numbered angles for each parallelogram.
15.
1
16.
2
3
38
17.
2
3
1
63
1 99
37
2
79
3
37,
26,
26
38, 43, 99
101, 79, 101
Determine whether the quadrilateral must be a parallelogram.
18.
19.
20.
21.
yes
no
x 2 Algebra Find the values of the variables for which ABCD must be a parallelogram.
yes
yes
22. B
(3y 20)
23. B
C
4x
(4y 4)
4x (2x 6)
A
x ≠ 29, y ≠ 28
6-4 and 6-5 Objectives
To use properties of
diagonals of rhombuses
and rectangles
To determine whether a
parallelogram is a
rhombus or a rectangle
To verify and use
properties of trapezoids
and kites
358
358
3y
D
C
x
2 3
3 3y
A
1
D
x ≠ 4, y ≠ 5
Each diagonal of a rhombus bisects two angles of the rhombus. The diagonals of a
rhombus are perpendicular.
The diagonals of a rectangle are congruent.
If one diagonal of a parallelogram bisects two angles of the parallelogram, then the
parallelogram is a rhombus. If the diagonals of a parallelogram are perpendicular,
then the parallelogram is a rhombus. If the diagonals of a parallelogram are
congruent, then the parallelogram is a rectangle.
The parallel sides of a trapezoid are its bases and the nonparallel sides are its legs.
Two angles that share a base of a trapezoid are base angles of the trapezoid.
Chapter 6 Chapter Review
Alternative Assessment
Name
The base angles of an isosceles trapezoid are congruent. The diagonals of an
isosceles trapezoid are congruent.
Class
L4
Date
Alternative Assessment
Form C
Chapter 6
TASK 1
The diagonals of a kite are perpendicular.
a. If ABCD is a parallelogram, list everything you know about the sides
and angles in the figure.
Find the measures of the numbered angles in each quadrilateral.
b. Which of the following conditions are sufficient, individually, to
guarantee that ABCD is a parallelogram?
A. AB ⬵ CD and BC 6 AD
B. BD # AC
C. BD and AC bisect each other.
D. BE ⬵ EC and AE ⬵ ED
E. ⬔BAD ⬵ ⬔BCD and ⬔ABC ⬵ ⬔ADC
F. AB ⬵ CD and BC ⬵ AD
25.
2 3
56
1
26.
2
1
1 60 3
60, 90, 30
124, 28, 62
13
C
in.
28. D
Draw a Venn diagram showing the relationships among squares, rectangles,
rhombuses, and parallelograms.
E
A
To prove theorems using
figures in the coordinate
plane
10
B
A
26 in.
To name coordinates of
special figures by using
their properties
D
C
7f
t
E
6-6 and 6-7 Objectives
29.
E1
2f
cm
t
A
B
20 cm
D
TASK 2
90, 25
C
A
2
65
Find AC for each quadrilateral.
27. D
C
E
© Pearson Education, Inc. All rights reserved.
24.
B
B
Geometry Chapter 6
31
Form C Test
19 ft
In coordinate proofs, it generally is good practice to center the figure on the origin
or place a vertex at the origin and one side of the figure on an axis.
The segment that joins the midpoints of the nonparallel sides of a trapezoid is the
midsegment of the trapezoid. It is parallel to the bases and half as long as the sum
of the lengths of the bases.
The formulas for slope, midpoint, and distance are used in coordinate proofs.
Give the coordinates of point P without using any new variable.
30. rectangle
y
(0, b)
31. square
P
x
(a, 0)
O
y
32. parallelogram
y
(b, c)
P
x
(c, 0)
(c, 0) O
(a, b)
(0, c)
(0, c)
x
(a, 0)
O
(a – b, c)
Complete each coordinate proof.
33a. –1
b. 1
c. The prod. of the
slopes is –1.
Spanish Quarter 2 Test - Forms A, B ELL
Name
33. The diagonals of a square are perpendicular.
F(0, a)
Quarter 2 Test — Forms A, B
x
H(a, 0)
I
Graph
quadrilateral
ABCD. Then
Q
V determine
R name for
5.
6. Qthe most precise
each quadrilateral.
5 cm
b2
Prove: AC > BD
Vertex A is at the origin with coordinates (0, 0).
Name B as (a, 0), C as (a. 9, b), and D as b. 9.
AC = c. 9 and BD = d. 9. So, AC = e. 9,
and AC > BD.
T
(4x 40)
x
A
B
U
5 cm
S
R
y
V
T
Find the values of the variables for each figure.
11.
12. y
8. x
9. (3x)
(4x 40)
(2x)
X
V
U
7. Q
10. AC = 7x - 15, BD = 4x + 15
4 in.
A
B
z
2m
S 33)
(2x X
V
D
C
24
13.
10. AC = 7x - 15, BD = 4x + 15
y
(3x)
A x
B
13
(2x)
(3x 10)
34
(2x 33)
D
Give the coordinates for points D and E without using any new variables.
11. find the coordinates of the midpoint
12.
13.
Then
of DE
y .
x
C
24
(3x)
14. rectangle
15. isosceles trapezoid
13
x
16. rhombus
(2x)
G (a, c)
E
(3x 10)
E
34 D
F (a, b)
E
D
C (a, 0)
F (b, 0)
Give the coordinates for points D and E withoutDusing anyGnew
(a variables.
c, 0)
Then find the coordinates of the midpoint of DE.
14. rectangle
15. isosceles trapezoid
G (a, c)
E
E
D
B (0, b)
16. rhombus
D
F (a, b)
Form A TestE
Geometry Chapter 6
C (a, 0)
F (b, 0)
D
Chapter 6 Chapter Review
U
4. A(0, 6), B(3, 3), C(0, -5), D(-3, 3)
3 in.
(2x)
T
y
7. Q
4 in.
V2. A(1, 2), B(3, 8), C(5, 2), D(3, -4)
z
2m
3 in.
4 cm
1. A(2, 3), B(-4, 3), C(-2, 6), D(1, 6)
Find QV in each parallelogram.
Find the values of the variables for each figure.
Q
V
5.
6. Q
8.
9. (3x)
C
Form A
Chapter 6
3. A(-1,
4), B(2, 4), C(2,
0), D(-1, 0)
T
U
D
L3
Date
4. A(0, 6), B(3, 3), C(0, -5), D(-3, 3)
L2
Find QV in each parallelogram.
4 cm
Given: Rectangle ABCD
Form A
2. A(1, 2), B(3, 8), C(5, 2), D(3, -4)
1. A(2, 3), B(-4, 3), C(-2, 6), D(1, 6)
Chapter
Test
3. A(-1, 4), B(2,
4), C(2, 0), D(-1, 0)
Prove: FH ' GI
Date
Graph quadrilateral ABCD. Then determine the most precise name for
each
quadrilateral.
Name
Class
© Pearson
Education, Inc. All rights reserved.
© Pearson Education, Inc. All rights
reserved.
c. "a2 1 b2
1
d.
e. BD
G(a, a)
34. The diagonals of a rectangle are congruent.
34a. a
b. (0, b)
Class
Chapter Test
Quarter
2 Test - Forms D, E
Chapter 6
y
Given: Square FGHI with vertices I(0, 0),
H(a, 0), G(a, a), and F(0, a)
The slope of FH is a. 9. The slope of GI is
b. 9. FH ' GI because c. 9.
"a2
P
G (a c, 0)
27
B (0, b)
359
Geometry Chapter 6
Form A Test
27
359