Download 6.2 parallelograms 2016 ink.notebook

6.2 parallelograms 2016 ink.notebook
January 11, 2017
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6.2
Parallelograms
Don't forget
to put it in
the table of
contents
Lesson Objectives
Standards
6.2 Parallelograms
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Lesson Notes
Lesson Objectives
Standards
Lesson Notes
After this lesson, you should be able to successfully recognize and apply the properties of parallelograms.
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6.2 parallelograms 2016 ink.notebook
Lesson Objectives
Standards
January 11, 2017
Parallelogram
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.).
A quadrilateral in which both pairs of opposite sides are parallel
Parallelogram
Parallelogram
Cut this
piece off
A quadrilateral in which both pairs of opposite sides are parallel
Find the value of each variable.
Opposite sides Consecutive angles
are congruent. are supplementary.
1.
A quadrilateral in which both pairs of opposite sides are parallel
Cut this
piece off
4.
70¡
110¡
110¡
70¡
5.
2.
Opposite angles Diagonals bisect
are congruent. each other.
8x
112¡
3.
If a parallelogram
has 1 rt Ú's, then
it has 4 rt angles.
6.
Each diagonal separates
the parallelogram into 2
¤ è's.
A
C
B
D
èABC ¤ èDCB
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6.2 parallelograms 2016 ink.notebook
Opposite sides
are congruent.
Find the value of each variable.
January 11, 2017
4.
Consecutive angles
are supplementary.
1.
70¡
110¡
110¡
70¡
Opposite angles
are congruent.
2.
5.
Diagonals bisect
each other.
6.
Each diagonal separates
the parallelogram into 2
¤ è's.
8x
112¡
If a parallelogram 3.
has 1 rt Ú's, then
it has 4 rt angles.
A
C
B
D
èABC ¤ èDCB
If each quadrilateral is a parallelogram, find the value of each variable.
2.
1.
3.
4.
12
3x°
2y
6.
5.
Explain why it is impossible for each figure to be a parallelogram.
7.
8.
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6.2 parallelograms 2016 ink.notebook
If each quadrilateral is a parallelogram, find the value of each variable.
1.
January 11, 2017
If each quadrilateral is a parallelogram, find the value of each variable.
4.
3.
2.
If each quadrilateral is a parallelogram, find the value of each variable.
5.
6.
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6.2 parallelograms 2016 ink.notebook
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Explain why it is impossible for each figure to be a parallelogram.
7.
8.
On the
Worksheet
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6.2 parallelograms 2016 ink.notebook
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Coordinate Geometry. Find the coordinates of the intersection of the diagonal of ãABCD with the given vertices.
A. A(3, 6), B(5, 8), C(3, –2), and D(1, –4)
Coordinate Geometry. Find the coordinates of the intersection of the diagonal of ãABCD with the given vertices.
B. A(–4, 3), B(2, 3), C(–1, –2), and D(–7, –2)
Find the value of each variable.
1.
HOMEWORK
R
2a
S
2b - 1
U
2.
b + 3
3a - 5
T
Practice WS on Parallelograms
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6.2 parallelograms 2016 ink.notebook
Find the value of each variable.
3.
Find the value of each variable.
4.
Use ãRSTU to find each measure or value.
7. mÚRST = _____
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6.
5.
Coordinate Geometry. Find the coordinates of the intersection of the diagonal of ãHJKL with the given vertices.
11. H(1, 1), J(2, 3), K(6, 3), L(5, 1)
8. mÚSTU = _____
9. mÚTUR = _____
10. b = ______
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6.2 parallelograms 2016 ink.notebook
Coordinate Geometry. Find the coordinates of the intersection of the diagonal of ãHJKL with the given vertices.
12. H(–1, 4), J(3, 3), K(3, –2), L(–1, –1)
14. DISTANCE Four friends live at the four corners of a block shaped like a parallelogram. Gracie lives 3 miles away from Kenny. How far apart do Teresa and Travis live from each other?
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13. CONSTRUCTION Mr. Rodriquez used the parallelogram at the right to design a herringbone pattern for a paving stone. He will use the paving stone for a sidewalk. If mÚ1 is 130, find mÚ2, mÚ3, and mÚ4.
Find the value of each variable.
15.
16.
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6.2 parallelograms 2016 ink.notebook
Find the value of each variable.
17.
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Answers:
18.
1. 2a = 3a – 5, a = 5, 2b – 1 = b + 3, b = 4 3. x – 2 = 19, x = 21, y + 1 = 26, y = 25 5. a + 14 = 6a + 4, a = 2, 9b + 8 = 10b + 1, b = 7 7. 125 9. 125 11. (3.5, 2) 13. mÚ2 = 50, mÚ3 = 130, mÚ4 = 50 15. 3a – 4 = a + 2, a = 3, b + 1 = 2b, b = 1 17. x – 3 = 15, x = 18, y + 3 = 12, y = 9
In the book, do pages 403 – 407, problems: 9 – 12, 15 – 20, 46, 47
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