4.2 Quadrilaterals
Rectangles, Rhombuses, and Squares
Name:_______________________________
A rectangle is a parallelogram with four right angles.
1. Quadrilateral RECT is a rectangle. List all right triangles in the figure and sketch each.
Explain how you know the triangles are congruent.
R
E
G
C
T
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2. Complete the theorem.
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The diagonals of a rectangle are ________________________.
3. Explain
how
you know
the theorem in item 2 is true.
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4. List all the properties of rectangles. Begin with properties of a parallelogram.
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5. Given quadrilateral TGIF is a rectangle and TX = 13 and mGTI = 64. Use the properties of a rectangle to find
each of the following.
a. XI = ________
T
F
64
b. FG = ________
13
X
c. XG = ________
d. mFTI = ________
G
I
e. mTFG = ________
4.2 Quadrilaterals
A rhombus is a parallelogram with four congruent sides.
F
6. Given quadrilateral EFGH is a rhombus.
a. List the three triangles that are congruent to HXE. Explain why
you know they are congruent.
X
E
G
b. Explain why EFX ≌ GFX and HGX ≌ FGX.
H
c. Complete the theorem.
Each diagonal of a rhombus __________________________________________________________________________.
d. Explain why mEXF = 90.
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The diagonals
a rhombus are ____________________________________________.
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7. List all the properties of a rhombus. Begin with properties of a parallelogram.
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8. Given quadrilateral UTAH is a rhombus. Use the properties of a rhombus to find each of the following.
U
a. Solve for x if mUZT = (4x + 18).
b. Solve for x & y if
Z
H
T
UT = 5x + 4
TA = 2x + y
HA = 2y – 8
UH = 24
c. Solve for x if mZAT = (6x) and mZTA = (10x + 10).
A
4.2 Quadrilaterals
A square is a parallelogram with four right angles and four congruent sides.
9. Complete each of these alternate definitions of a square.
S
a. A square is a rectangle with
Q
U
_____________________________________.
R
A
b. A square is a rhombus with
_____________________________________.
10. List all the properties of a square.
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11. Given quadrilateral BKFT is a square. Use the properties of a square to find each of the following.
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B
3
2
b. m2 = ________
1
4
T
m1 = ________
c. m3 = ________
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d. m4 = ________
5
F
e. m5 = ________
12. The perimeter of square MNOP is 72 inches. Find the length ̅̅̅̅̅
𝑀𝑁 and diagonal ̅̅̅̅̅
𝑀𝑂. Leave your answer in exact
form.
4.2 Quadrilaterals
Rectangles, Rhombuses, and Squares
Name:____________________________________
Homework
Date :__________________ Period: ________
Find the measure of each numbered angle in the quadrilaterals below.
1. Rectangle DLRP
G
2. Rhombus GDSM
m1 = _____
L
D
3
m2 = _____
4
m3 = _____
Q
2
m2 = _____
5
1
R
P
m5 = _____
M 1
5
m4 = _____
27°
S
m5 = _____
3. Square TRLJ
4 D
m3 = _____
58°
m4 = _____
23
m1 = _____
4. Rhombus QVCH
T
V
R
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2
5
m1 = _____
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m2 = _____
Q
m1 = _____
3
2
70°
m2 = _____
1
m3 = _____
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4
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m4 = _____unlimited amount
J
m3 = _____
m5 = _____
m5 = _____
4
3
m4 = _____
H
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Solve for the indicated measures.
5. MATH is a square. ML = 2x + 10,
HL = 6x – 14, find x and HA.
6. ABCD is a rhombus. Find the values of
x, y, and z.
B
A
M
A
L
56°
y°
H
T
4z°
2x°
D
C
C
4.2 Quadrilaterals
7. ABCD is a rectangle. Find the indicated
angle measures.
A
8. ABCD is a square. If mCAB = (4y + 1)°,
and mAEB = (5x + 55)°, solve for x and y.
B
B
65°
C
E
E
D
C
mBAD = _________
mBDC = _________
mBCE = _________
mAEB = _________
A
D
9. RSTV is a rectangle. If mVRT = (7x)°, and
mRTV = (8x)°, find x and mRTV.
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10. RSTW is a rectangle. The diagonals
intersect at Z. If RZ = 2x + 5,
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SW = 5x –for
20, find
x and ZW.
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̅̅̅̅̅ and 𝑁𝑃
̅̅̅̅
11. MNOP is a rhombus with diagonals 𝑀𝑂
intersecting at T. If mTMP = (4x + 40)°, and
mTPM = (11x + 20)°, solve for x and find
mTOP.
12. GHIJ is a rhombus. The diagonals
intersect at K. If GK = 7, and HK = 24,
find HI.
13. Which statement is NOT true?
A. All squares are rhombuses.
B. All rhombuses are parallelograms.
C. The diagonals bisect each other in squares, rhombuses, and rectangles.
D. The diagonals are perpendicular in squares, rhombuses, and rectangles.
documents.