6.5 proving special parallelograms 2016 ink.notebook
January 23, 2017
Lesson Objectives
Standards
Lesson Notes
Page 28
6.5 Proving Special
Parallelograms
6.5 Proving Special Parallelograms
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Lesson Objectives
Standards
Lesson Notes
Lesson Objectives
After this lesson, you should be able to successfully apply the properties a rhombus and a square to prove they are that figure.
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Standards
Lesson Notes
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G.CO.11 Prove theorems about parallelograms.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
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6.5 proving special parallelograms 2016 ink.notebook
Quadrilaterals
January 23, 2017
Determine whether ABCD is a rectangle, rhombus or a square.
B
The vertices are A(–3, –2), B(1, 1), C(5, –3), and D(1, –7).
C
A
D
If the diagonals are congruent, then it is a rectangle. If the slopes show the diagonals are perpendicular, then it is a square, which is also a rhombus.
If the slopes show the diagonals are perpendicular, but the diagonals are NOT congruent, then it is just a rhombus.
AC = BD = slope of AC =
slope of BD =
Determine whether ABCD is a rectangle, rhombus or a square.
The vertices are A(–3, –2), B(1, 1), C(5, –3), and D(1, –7).
B
A
C
If both pairs of opposite sides are congruent, then it is a parallelogram.
If all sides are congruent, then it is a rhombus.
Distances
If the slopes show the diagonals are perpendicular, then it is a square, which is also a rhombus and a rectangle.
D
Slopes
AB = AB = BC =
BC =
CD = CD = AD =
AD =
2
6.5 proving special parallelograms 2016 ink.notebook
January 23, 2017
Given each set of vertices, determine whether ãABCD is a parallelogram, rectangle, rhombus, or square. List all that apply. Explain.
1. A(0, 2), B(2, 4), C(4, 2), D(2, 0)
y
On the
Worksheet
x
Given each set of vertices, determine whether ãABCD is a parallelogram, rectangle, rhombus, or square. List all that apply. Explain.
2. A(–2, 1), B(–1, 3), C(3, 1), D(2, –1)
Given each set of vertices, determine whether ãABCD is a parallelogram, rectangle, rhombus, or square. List all that apply. Explain.
y
3. W(–3, –3), X(1, –6), Y(5, –3), Z(1, 0)
y
x
x
3
6.5 proving special parallelograms 2016 ink.notebook
January 23, 2017
Given each set of vertices, determine whether ãABCD is a parallelogram, rectangle, rhombus, or square. List all that apply. Explain.
4. Q(–5, 12), R(5, 12), S(–1, 4), T(–11, 4)
BOOK Work p. 431 – 434: HOMEWORK
y
5, 6, 19, 21, 22, 46, 51, 53, 55 – 61
x
4
6.5 proving special parallelograms 2016 ink.notebook
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y
y
x
x
y
y
x
x
5
6.5 proving special parallelograms 2016 ink.notebook
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6.5 proving special parallelograms 2016 ink.notebook
January 23, 2017
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