CHAPTER 5: QUADRILATERAL PROPERTIES
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Name
TI Nspire: Finding Properties of Quadrilaterals
Identifying Quadrilaterals
Constructing Quadrilaterals
Applying Properties of Parallelograms
Video: Transformational Proofs
Transformational Proofs
Chapter Review
Test
Name ________________________________
Completed?
Score ____/10
Name _______________________________
NR Geometry
TI Nspire: Finding Properties of Quadrilaterals
Chp 5 Wksht #1
Use the TI Nspire file titled quadrilateral_properties to complete this sheet. I WILL NOT be telling you
if you are right or wrong, so you must make sure you are accurate!
SIDE PROPERTIES
Opposite sides are ||
Opposite sides are 
Adjacent sides are 
4  sides
One pair opposite sides are ||
ANGLE PROPERTIES
Opposite angles are 
Consecutive ’s = 180
4  angles (90)
Both pairs of base angles 
DIAGONAL PROPERTIES
Diagonals bisect each other
Diagonals are 
Diagonals are 
Diagonals are  bisectors
Diagonals Create 2  Triangles
Shade in the properties that are held by the first 4 SHAPES.
What does this mean about all four of these quadrilaterals?
Kite
Isosceles
Trapezoid
Trapezoid
SQUARE
RHOMBUS
RECTANGLE
PARALLELOGRAM
Summary of Quadrilateral Properties
Name _______________________________
NR Geometry
Identifying Quadrilaterals
Chp 5 Wksht #2
15) Determine whether the statement is (A)lways, (S)ometimes, or (N)ever True.
a) The diagonals of a rectangle are congruent.
b) The diagonals of a parallelogram are perpendicular.
c) A parallelogram is a rhombus.
d) The diagonals of a rhombus bisect each other.
e) A rhombus is equilateral.
A
A
A
A
A
S
S
S
S
S
N
N
N
N
N
16) Classify the triangle as specific as you can (by side and by angle).
a) In rectangle ABCD where mDAC = 65,
c) In parallelogram ABCD where mDAE = 85 &
mDBC = 19
what type of  is DEA?
_____________________
what type of  is ADC?
_____________________
A
B
A
B
E
E
C
D
D
d) In square ABCD,
b) In rhombus ABCD where mEDA = 20,
what type of  is ADC?
_____________________
A
C
what type of  is DAB?
___________________
B
A
E
B
E
D
C
D
C
17) Determine the correct answers.
a) A square is a rectangle
b) A parallelogram is a rhombus
c) A rhombus is a square
d) A square is a parallelogram
Always
Always
Always
Always
Sometimes
Sometimes
Sometimes
Sometimes
Never
Never
Never
Never
17) Determine which quadrilateral has these properties? (Pick all the correct answers).
A (Parallelogram)
B (Rectangle)
C (Rhombus)
a) Diagonals are congruent
_______________________________
b) Equilateral
_______________________________
c) Diagonals bisect each other
_______________________________
D (Square)
Name _______________________________
NR Geometry
Constructing Quadrilaterals
Chp 5 Wksht #3
You will need the TI Nspire document titled quadrliaterals_constructions
1.) Advance to page 1.2
a.) Try to move segments, angles, etc. on each figure.
b.) Are the figures in the two panels squares? Why or why not.
c.) Which panel shows a construction and which shows a drawing? How do you know?
2.) Construct a parallelogram (together)
3.) Construct any two other shapes in the document. Make sure I can’t “break” them.
4.) Tell me when you have finished so I can collect the file from you.
Name _______________________________
NR Geometry
Applying Properties of Parallelograms
Chp 5 Wksht #4
1. Quadrilateral ABCD is a parallelogram.
a) mBAC = 54,
b) mADC = 78,
find mDCA = _________
find mDAB = _________
c) mDCB = 142 & mDCA = 37
find mBAC= _________
d) mABC = 73 & mDBA = 31
find mDBC = _________
e) AE = 14 cm & DE = 18 cm,
find EB = __________
f) EC = 10 cm & EB = 15 cm,
find AC = __________
2. Quadrilateral ABCD is a rhombus.
a) mADE = 27,
find mDAE = _________
find mABD = _________
E
C
D
b) mADE= 74
find mDAE= _________
find mBEC= _________
A
c) mAEB= 144,
find mCAB = _________
d) mBCA = 78
find mDAC = _________
e) DE = 9cm,
find AC = __________
f) AD= 6 cm & DC = 8 cm,
find AE = __________
4. Find the value for the variables.
a) Parallelogram
b) Parallelogram
x = ________
x = _______
A
B
E
3x - 3
D
C
D
d) Rhombus
x = ________
A
B
B
E
c) Rhombus
x = _________
A
C
A
f) AD = 13 cm & BD = 24 cm,
find AC = __________
3. Quadrilateral ABCD is a rectangle.
a) mBAC = 27,
find mACB = _________
find mDAC = _________
D
C
B
d) mDAB = 140
find mADE = _________
e) AE = 3 cm & DE = 4 cm,
find DB = __________
find AD = __________
39°
42°
E
D
b) mCAB = 71,
find mCEB = _________
c) mABC = 64
find mABE= _________
E
B
A
B
A
28°
E
5x - 6
D
34 cm
D
3x - 5
E
35°
5x - 15
B
C
C
C
5. Given parallelogram ABCD, determine the measurements.
a) mDCB = ___________
b) mADC = ___________
c) mADB = ___________
d) mABD = ___________
e) AD = ___________
f) AB = ___________
A
81°
E
D
B
10 cm
30°
24 cm
C
6. Given rectangle ABCD and the given information to solve each problem.
a) AC = 4x – 54 and BD = 33 + 1x, find x = ______ & BD = _______
A
E
b) AC = 4x – 60 and AE = x + 5, find x = ______ & EC = ____________
c) mBAC = 4x + 12 and mDAC = 5x + 24, find x = _____ &
D
mDAC = _______
d) AE = 9 cm, DC = 15 cm, find AD = ___________ (2 decimal places)
e) mEAD = 63, mAED = 4x + 8, find x = ____________
7. Kites and Trapezoids
a)
b)
c)
d)
e)
f)
B
g)
C
Name _______________________________
NR Geometry
Video: Transformational Proofs
Chp 5 Wksht #5
1. Prove that opposite angles of a parallelogram are congruent.
a) Proof by Symmetry (Informal – Transformational Approach)
Given: Parallelogram ABCD
C
Prove that opposite angles of the parallelogram are congruent.
B
E
D
A
b) Proof by Congruent Triangles (Formal – Classic Approach)
Given: Parallelogram ABCD
C
Prove: A C, B  D
STATEMENT
ABCD is a parallelogram
B
REASON
Given
D
A


2. Prove that diagonals bisect each other in a parallelogram.
a) Proof by Symmetry (Informal – Transformational Approach)
Given: Parallelogram ABCD
C
Prove that diagonals bisect each other.
B
E
D
A
b) Proof by Congruent Triangles (Formal – Classic Approach)
Given: Parallelogram ABCD
C
Prove: DE  BE , CE  AE
STATEMENT
ABCD is a parallelogram
B
E
REASON
Given
A


D
Name _______________________________
NR Geometry
Transformational Proofs
Chp 5 Wksht #6
1. Given parallelogram ABCD, use a transformational approach to prove that the opposite sides are congruent.
C
B
E
D
A
2. Given rhombus ABCD, use a transformational approach to prove that diagonals are angle bisectors.
B
C
E
A
D
3. Given rectangle ABCD, use a transformational approach to prove that diagonals are congruent.
C
B
D
A
4. Given rhombus ABCD, use a transformational approach to prove that diagonals are perpendicular.
B
C
A
E
D
Name _______________________________
NR Geometry
Chapter Review
Chp 5 Wksht #7
Vocabulary:
Quadrilateral
Parallelogram
Kite
Trapezoid
Rectangle
Rhombus
Square
1. Which of the following is NOT a characteristic of all parallelograms?
A) Diagonal bisect each other
1. ________
B) Opposite angles are congruent
C) Diagonals are angle bisectors
D) Opposite sides are congruent
2. Which of the following is NOT a characteristic of all rectangles?
A) Consecutive angles are supplementary
C) Diagonals bisect each other
2. ________
B) Opposite angles are congruent
D) Diagonals are perpendicular
3. Which of the following is NOT a characteristic of all rhombi?
3. ________
A) Four congruent sides
B) Diagonals are angle bisectors
C) Diagonals are perpendicular
D) Diagonals are congruent
4. Which of the following group of quadrilaterals have diagonals that are perpendicular?
4. ________
A) Rhombus, Square
B) Rhombus, Parallelogram, Square
C) Rectangle, Square
D) Rectangle, Rhombus, Square
Determine whether the following are (T)rue or (F)alse.
5. A rhombus has four congruent angles.
T or F
6. A rectangle has diagonals that bisect each other.
T or F
7. Consecutive sides are congruent in a rectangle.
T or F
8. If a parallelogram has 4  angles, then it must be a square.
T or F
9.
Use the diagram on the right to answer questions 1-16.
17.
18.