Name______________________________________________
Date_________________ Period__________
Classwork 8 Unit 2 --- Rhombuses, Rectangles, Squares & Parallelograms
Standard G.CO.11 Prove theorems about parallelograms.
For problems 1-7, answer (T) True or (F) False.
____ 1. Every rhombus is a parallelogram.
____ 2. The diagonals of a rhombus bisect each other.
____ 3. The diagonals of a rhombus are congruent.
____ 4. The diagonals of a rhombus are perpendicular to each
other.
____ 5. The consecutive angles of a rhombus are
congruent.
____ 6. The consecutive sides of a rhombus are congruent.
____ 7. A rhombus and one of its diagonals form two isosceles triangles.
8.
Complete the table. Place an X under the name of each figure for which the property is true.
Parallelogram
Rhombus
Rectangle
The diagonals are perpendicular
The figure has four right angles
The opposite sides are congruent
The diagonals are congruent
The figure has four congruent sides
The diagonals bisect each other.
The consecutive angles are supplementary
Each diagonal bisects a pair of opposite angles
The figure has exactly four lines of symmetry
The figure is a rectangle
9.
MNPQ is a rhombus. Find the measure of each angle.
a. m
= ________
Square
N
M
2
d. m
= ________
b. m
e. m
= ________
= ________
c. m
f. m
= ________
4
3
= ________
35°
10.
GHJK is a rhombus, with GJ = 42. Find the length of each segment.
P
Q
H
G
a. GH = ________
b. HJ = ________
d. LH = ________
e. KH = ________
1
c. LJ = ________
58
L
40
11.
ABCD is a rhombus. Find each angle measure or segment length.
a.
m
= ________
b.
m
c.
m
= ________
d.
m
e.
m
= ________
f.
AD = ________
g.
BD = ________
h.
ED = ________
EFGH is a rhombus, with m
60°
= ________
and m
C
1
= ________
26
2
A
12.
J
B
K
. Find x and m
3
E
4
D
13.
a. m
= ________
b. m
= ________
c. m
B
A
ABCD is a rectangle, with AC = 18. Find each length or angle measure.
54°
1
2
= ________
3
d. m
= ________
e. m
= ________
g. m
= ________
h. AE = ________
f. m
E
= ________
6
4
i. DB = ________
5
C
D
14.
GHKL is a rectangle that is not a square. Answer (T) True or (F) False.
H
G
____ a. GHKL and its diagonals form four congruent triangles.
1
____ b. GHKL and its diagonals form four isosceles triangles.
____ c.
2
____ d.
____ e.
is a line of symmetry.
____ f.
M
L
K
____ g.
A
15.
B
Complete the proof to show a rhombus and its diagonals form four right triangles.
Given: ABCD is a rhombus
Prove:
E
are right triangles
Statements
Reasons
1. ABCD is a rhombus
1.
2.
2.
3.
3.
4.
are right triangles
C
D
4.
G
H
1
16.
Complete the proof:
Given: GHIJ is a rhombus
Prove:
3
J
Statements
Reasons
1. GHIJ is a rhombus
1.
2.
2. A rhombus is a parallelogram
3.
3.
4.
4.
5.
5. In a rhombus, each diagonal bisects opposite angles
6.
6.
2
I