Determining Quadrilateral Properties using Triangles & Transformations

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G.CO.11 ACTIVITY #1
NAME: _____________________
1
Determining Quadrilateral Properties using Triangles & Transformations
(Use patty paper and the triangles on the bottom of page 4 to complete these activities.)
1. SCALENE ACUTE TRIANGLE
Use two scalene acute triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
Diagram the quadrilateral
Transformation:
Rotation at Midpoint of Side (2)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (3)
Name of Quadrilateral
Name of Quadrilateral
Name of Quadrilateral
Parallelogram
____________________________
____________________________
Properties of the Quadrilateral
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• Consecutive ∠ = 180°
Properties of the Quadrilateral
Properties of the Quadrilateral
2. ACUTE ISOSCELES TRIANGLES
Use two acute isosceles triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
l
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Name of Quadrilateral
Name of Quadrilateral
Rhombus
____________________________
Properties of the Quadrilateral
• 4 ≅ Sides
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• Diagonal is an Angle Bisector
Properties of the Quadrilateral
G.CO.11 ACTIVITY #1
2
3. EQUILATERAL TRIANGLES
Use two equilateral triangles to form a quadrilateral.
Transformation:
Rotation at Midpoint of Side (1)
Diagram the quadrilateral
Properties of the Quadrilateral
Name of Quadrilateral
____________________________
4. RIGHT ISOSCELES TRIANGLES
Use two right isosceles triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
l
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Name of Quadrilateral
Name of Quadrilateral
Parallelogram
____________________________
Properties of the Quadrilateral
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• Consecutive ∠ = 180°
Properties of the Quadrilateral
Use four right isosceles triangles to form a quadrilateral
Diagram the quadrilateral
Transformation:
3 Rotations at the 90°° vertex
Name of Quadrilateral
____________________________
Properties of the Quadrilateral
G.CO.11 ACTIVITY #1
3
5. RIGHT SCALENE TRIANGLES
Use two right scalene triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
Diagram the quadrilateral
Transformation:
Rotation at Midpoint of Side (3)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Name of Quadrilateral
Name of Quadrilateral
Name of Quadrilateral
Rectangle
____________________________
____________________________
Properties of the Quadrilateral
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• 4 ≅ Angles
Properties of the Quadrilateral
Properties of the Quadrilateral
Use four right scalene triangles to form a quadrilateral
Diagram the quadrilateral
Transformation:
3 Reflections on Side
Name of Quadrilateral
____________________________
Properties of the Quadrilateral
G.CO.11 ACTIVITY #1
4
SUMMARIZE THE PROPERTIES FOR EACH QUADRILATERAL
PARALLELOGRAM
RECTANGLE
C
B
A
D
D
B
C
E
E
A
RHOMBUS
B
A
E
C
D
Properties of a Parallelogram
SQUARE
B
A
E
C
D
Properties of a Square
Properties of a Rectangle
Properties of a Rhombus
G.CO.II ACT|V|TY #7
NAME:
Determining Quadrilateral Properties using Triangles & Transformations
1. SCALENE ACUTE TRIANGI!
Use
two scalene acute triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
Diagram the quadrilateral
o
'u
t
*/
,/f
r.
o
Transformation:
Rotation at Midpoint of Side (2)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (3)
Name of Quadrilateral
Name of Quadrilateral
Name of Quadrilateral
Parallelogram
Properties of the Quadrilateral
Opposite Sides =
Opposite Angles =
Opposite Sides I I
.
o
.
o
ConsecutiveZ=L80o
pavr.t\UL
P.r"*tLc\ oev-ua*
Properties of the Quadrilateral
. vfPe't;k- qidc y
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o opprrl\< S,\,eg /l
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n A1poqif,q- Sl'dce 0
o {gra-1tl
u[} r*-- colVc = |fu"
a (etgLc,,l 1*t'-- ac*1Q-S = |fu"
2. ACUTE ISOSCELES TRIANGLES
Use
two acute isosceles triangles to form a quadrilateral.
Diagram the
quadrilateral
Diagram the quadrilateral
o
ti
e
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Name of Quadrilateral
Name of Quadrilateral
Rhombus
Properties of the Quadrilateral
o
.
.
.
o
4 = Sides
Opposite Sides =
Opposite Angles =
Opposite Sides I I
Dia8onal is an Angle Bisector
?rrn*ttz\ Dhta.\/\.s
Properties of the Quadrilateral
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c 6ppolilc- *1k'/ ?
.
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Properties of the Quadrilateral
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'
lto"
G.CO.17 ACT|V|TY #1
2
3. EQUITATERAL TRIANGLES
Use
two equilateraltriangles to form a quadrilateral.
Diagram the quadrilateral
Transformation:
Rotation at Midpoint of Side (1)
Use
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. op potiE <--1v9 +
. 6 ppor,'.k- {d'r il
" DTn t^u( ) r a)\- avy k- bigol*
Name of Quadrilateral
4. RIGHT
Properties of the Quadrilateral
ISOSCETES TRIANGLES
two right isosceles triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Name of Quadrilateral
Name of Quadrilateral
Sa vaxL-
Parallelogram
Properties of the Quadrilateral
Opposite Sides =
Opposite Angles =
Opposite Sides | |
.
.
.
o
Use
ConsecutiveZ=L80o
Properties of the Quadrilateral
'') Y
-q;
9if,cs
a.rc1let
G"'\
.6pp 9:d-E Z
' opp drTlV e
,
oQP l7
"
Dro7?zrq,l
d-e-;
//
L bltruf^-'
four right isosceles triangles to form a quadrilateral
Diagram the quadrilateral
Transformation:
3 Rotations at the 90o vertex
,ror$",
? Ivr
Name of Quadrilateral
5a vu*rz-
of the Quadrilaterat
o
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dt 1
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-n*1, bi*ul.#
G.CO.II ACT|V|TY #1
3
5. RIGHT SCALENE TRIANGLES
Use
two right scalene triangles to form a quadrilateral.
Diagram the quadrilateral
Diagram the quadrilateral
Diagram the quadrilateral
Transformation:
Rotation at Midpoint of Side (3)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Name of Quadrilateral
Name of Quadrilateral
Name of Quadrilateral
.t
s
Properties of the Quadrilateral
Opposite Sides =
Opposite Angles =
Opposite Sides | |
4 = Angles
.
.
.
o
Properties of the Quadrilateral
a-v"c\k-loq,r,*-
Properties of the Quadrilateral
o op^,r,\- sides 2
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Use
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Rectangle
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four right scalene triangles to form a quadrilateral
Diagram the quadrilateral
Transformation:
3 Reflections on Side
Properties of the Quadrilateral
-J":
.rl=it'
- &lp ,iL*9 2
Name of Quadrilateral
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Z Y
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G.CO.71
ACfMffY#7
4
SUMMARIZE THE PROPERTIES FOR EACH QUADRILATERAL
PARATLETOGRAM
RECTANGTE
RHOMBUS
Properties of a Parallelogram
Properties of a Rectangle
Properties of a Rhombus
,o?P sivr il
. opf tid-E 2
)
+
"-< -'"+Lt Y
lr*:;q'^de
.QPPZY
'tvtxSnutlt"*L=(8o"
. T'to1ea,r.r.l9 btY"l carh ofuJ
\
t >a
(eu)
SQUARE
? ?o''-q'$t'l
oclt'^
-
Wc+**1W
? n, P*'\)cJ
Rigt*Seelme AcutehosceleB Rffilsosceles
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tu&
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Properties of a Square
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ptrdlaterat
G.CO.11 WORKSHEET #1
NAME: ____________________
1
COMPLETE THE CHART BY PLACING A CHECK IF THE QUADRILATERAL HAS THAT PROPERTY.
PROPERTY
Opposite Sides are
Parallel
Opposite Sides are
Congruent
Opposite Angles
are Congruent
Consecutive Angles
are Supplementary
Four Congruent
Angles (4 Right ∠’s)
Four Congruent
Sides
Diagonals Bisect
each other
Diagonals are
Congruent
Diagonals are Angle
Bisectors
Diagonals are
Perpendicular
PARALLELOGRAM
RECTANGLE
RHOMBUS
SQUARE
COMPLETE THE VENN DIAGRAM. If the Universal Set is Quadrilaterals, name and create boundaries for the
following: Parallelogram, Square, Rectangle, and Rhombus.

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