# 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.
Transformation:
Rotation at Midpoint of Side (2)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (3)
Parallelogram
____________________________
____________________________
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• Consecutive ∠ = 180°
2. ACUTE ISOSCELES TRIANGLES
Use two acute isosceles triangles to form a quadrilateral.
l
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Rhombus
____________________________
• 4 ≅ Sides
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• Diagonal is an Angle Bisector
G.CO.11 ACTIVITY #1
2
3. EQUILATERAL TRIANGLES
Use two equilateral triangles to form a quadrilateral.
Transformation:
Rotation at Midpoint of Side (1)
____________________________
4. RIGHT ISOSCELES TRIANGLES
Use two right isosceles triangles to form a quadrilateral.
l
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Parallelogram
____________________________
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• Consecutive ∠ = 180°
Use four right isosceles triangles to form a quadrilateral
Transformation:
3 Rotations at the 90°° vertex
____________________________
G.CO.11 ACTIVITY #1
3
5. RIGHT SCALENE TRIANGLES
Use two right scalene triangles to form a quadrilateral.
Transformation:
Rotation at Midpoint of Side (3)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Rectangle
____________________________
____________________________
• Opposite Sides ≅
• Opposite Angles ≅
• Opposite Sides ||
• 4 ≅ Angles
Use four right scalene triangles to form a quadrilateral
Transformation:
3 Reflections on Side
____________________________
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.
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t
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r.
o
Transformation:
Rotation at Midpoint of Side (2)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (3)
Parallelogram
Opposite Sides =
Opposite Angles =
Opposite Sides I I
.
o
.
o
ConsecutiveZ=L80o
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2. ACUTE ISOSCELES TRIANGLES
Use
two acute isosceles triangles to form a quadrilateral.
Diagram the
o
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e
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
Rhombus
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.
.
.
o
4 = Sides
Opposite Sides =
Opposite Angles =
Opposite Sides I I
Dia8onal is an Angle Bisector
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G.CO.17 ACT|V|TY #1
2
3. EQUITATERAL TRIANGLES
Use
two equilateraltriangles to form a quadrilateral.
Transformation:
Rotation at Midpoint of Side (1)
Use
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4. RIGHT
ISOSCETES TRIANGLES
two right isosceles triangles to form a quadrilateral.
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
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Parallelogram
Opposite Sides =
Opposite Angles =
Opposite Sides | |
.
.
.
o
Use
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four right isosceles triangles to form a quadrilateral
Transformation:
3 Rotations at the 90o vertex
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G.CO.II ACT|V|TY #1
3
5. RIGHT SCALENE TRIANGLES
Use
two right scalene triangles to form a quadrilateral.
Transformation:
Rotation at Midpoint of Side (3)
Transformation:
Rotation at Midpoint of Side (1)
Transformation:
Rotation at Midpoint of Side (2)
.t
s
Opposite Sides =
Opposite Angles =
Opposite Sides | |
4 = Angles
.
.
.
o
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Rectangle
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four right scalene triangles to form a quadrilateral
Transformation:
3 Reflections on Side
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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
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SQUARE
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Rigt*Seelme AcutehosceleB Rffilsosceles
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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.
```