Download Summary of Quadrilateral Properties

Name: ____________________________________________________________
Day 9: Quadrilaterals Review
Date: __________
Geometry CC (M1TE)
Summary of Quadrilateral Properties
SQUARE
RHOMBUS
RECTANGLE
PARALLELOG
RAM
Fill in the Quadrilateral Family Tree
SIDE PROPERTIES
Opposite sides are ||
Opposite sides are 
Adjacent sides are 
4  sides
ANGLE PROPERTIES
Opposite angles are 
Consecutive ’s = 180
4  angles (90)
DIAGONAL PROPERTIES
Diagonals bisect each other
Diagonals are 
Diagonals are 
Diagonals are  bisectors
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Determine if the following are (T)rue or (F)alse
1. A rhombus has congruent diagonals.
T or F
2. An isosceles trapezoid is not a parallelogram.
T or F
3. A square is parallelogram.
T or F
4. A rectangle has opposite sides that are parallel
T or F
5. A quadrilateral is any 5 sided polygon.
T or F
6. All parallelograms are squares.
T or F
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Multiple Choice Practice
7. Which statement cannot be used alone to prove that a quadrilateral is a rectangle?
(1)The quadrilateral is a parallelogram with congruent diagonals.
(2)The quadrilateral is a parallelogram with one right angle
(3)Pairs of opposite angles in the quadrilateral are congruent.
(4)All angles in the quadrilateral are right angles.
8. Quadrilateral MATH has diagonals MT and AH . Which information is not sufficient to prove MATH is a
parallelogram?
1)
2)
3)
4)
MA  TH and AT  MH
MA  TH and MA || TH
MT and AH bisect each other.
MA  TH and AT || MH
9. Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have diagonals
that bisect the angles?
(1)
(2)
(3)
(4)
the rhombus, only
the rectangle and the square
the rhombus and the square
the rectangle, the rhombus, and the square
10. Which reason could be used to prove that a parallelogram is a rhombus?
(1)
(2)
(3)
(4)
Diagonals are congruent.
Opposite sides are parallel.
Diagonals are perpendicular.
Opposite angles are congruent.
11. A parallelogram must be a rectangle when its
1)
2)
3)
4)
diagonals are perpendicular
diagonals are congruent
opposite sides are parallel
opposite sides are congruent
12. Which statement is false?
1) All parallelograms are quadrilaterals.
2) All rectangles are parallelograms.
3) All squares are rhombuses.
4) All rectangles are squares.
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13. A builder is building a rectangular deck with dimensions of 16 feet by 30 feet. To ensure that the sides form 90°
angles, what should each diagonal measure?
1)
2)
3)
4)
16 ft
30 ft
34 ft
46 ft
14. Given a quadrilateral ABCD. What criteria can be used to determine if ABCD is a rhombus?
(1) AB || CD, BC || DA and AB @ CD
(2) AB || CD and AB @ BC
(3) AB @ BC and BC @ CD
(4) AB || CD, BC || DA and AB @ BC
15. The cross section of an attic is in the shape of an isosceles trapezoid, as shown in the accompanying figure. If the
height of the attic is 6 feet,
feet, and
feet, find the length of
.
16. Parallelogram ABCD, mDBC = 43 o and mDCB = 57o find mDBA.
B
C
Y
A
D
17. In the accompanying diagram of rectangle ABCD, mBCA  40o , find mAED .
18. Quadrilateral CDEF is a square. Side CD = 2x + 12 and DE = 5x – 24. Find the perimeter of CDEF. Explain how you
arrived at your solution.
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19. Quadrilateral EFGH is a rhombus and you are given that mFGH= 50 o find the missing information below.
a) mHGX = _________
F
b) mGXH = _________
G
c) mXHG = _________
X
You are also given that FH = 10 cm & GE = 24 cm in rhombus EFGH
E
d) EH = __________
H
---------------------------------------------------------------------------------------------------------------------------------------------------------------20. Given rectangle ABCD below and E is the midpoint of BC , prove that EA  ED
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21. In the diagram of parallelogram WXYZ below WB ^ ZY , YA ^ WZ , AZ @ BZ .
Prove: WXYZ is a rhombus.
Statements
Reasons
1. Parallelogram WXYZ below WB ^ ZY , YA ^ WZ ,
2.
1. Given
3. YAZ  WBZ
3.
4. AZ @ BZ
5.
4. Given
6. WBZ  YAZ
6.
7. WZ  YZ
7.
8.WXYZ is a rhombus
8.
2. Perpendicular lines form right angles
5.Reflexive Property
22. Alex says, “If ABCD is a parallelogram, then ABCD is a rectangle.” Sketch a quadrilateral ABCD that shows that Alex’s
statement is not always true. Your sketch must show the length of each side and the measure of each angle for the
quadrilateral you draw.
23. What is the length of the side of a rhombus whose diagonals are 16 and 30?
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Name: ____________________________________________________________
Day 9: Quadrilaterals Review Homework
Date: __________
Geometry CC (M1TE)
1. In the diagram of parallelogram ABCD shown below, DC is extended to E, and BE is drawn such that BC  BE . If
mA  112o what is mCBE .
2. In rhombus ABCD below, what is mÐBDA ? Explain your solution.
3. Complete the following proof.
Given: Rectangle ABCD, with N the midpoint of CD
Prove: BN  AN
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