6.2 parallelograms 2016 ink.notebook€¦ · 6.2 parallelograms 2016 ink.notebook 1 January 11, 2017 Page 15 6.2 Parallelograms Don't forget to put it in the table of contents Page

6.2 parallelograms 2016 ink.notebook

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January 11, 2017

Page 15

6.2 Parallelograms

Don't forget to put it in the table of contents

Page 16

Lesson Objectives Standards Lesson Notes

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6.2 Parallelograms

Lesson Objectives

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Lesson NotesStandards

After this lesson, you should be able to successfully recognize and apply the properties of parallelograms.


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Lesson Objectives 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.).

ParallelogramA quadrilateral in which both pairs of opposite sides are parallel

Opposite sides are congruent.

Opposite angles are congruent.

Consecutive angles are supplementary.

70°

110° 70°

110°

Diagonals bisect each other.

If a parallelogram has 1 rt ⁄'s, then it has 4 rt angles. A

C

B

D

Each diagonal separates the parallelogram into 2 § Ë's.

ËABC § ËDCB

ParallelogramA quadrilateral in which both pairs of opposite sides are parallel

ParallelogramCut this piece off Cut this

piece off

8x

112°

Find the value of each variable.

1.

3.

2.

4.

5.

6.

A quadrilateral in which both pairs of opposite sides are parallel


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Opposite sides are congruent.

Opposite angles are congruent.

If a parallelogram has 1 rt ⁄'s, then it has 4 rt angles.

8x

112°


1.

3.

2.

Consecutive angles are supplementary.

70°

110° 70°

110°

Diagonals bisect each other.

A

C

B

D

Each diagonal separates the parallelogram into 2 § Ë's.

ËABC § ËDCB

4.

5.

6.

If each quadrilateral is a parallelogram, find the value of each variable.

1. 2.

3. 4.

3x°2y12

5. 6.

Explain why it is impossible for each figure to be a parallelogram.

7. 8.


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1. 2.3.


4.


5.6.


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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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Coordinate Geometry. Find the coordinates of the intersection of the diagonal of „ABCD 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 „ABCD with the given vertices.

B. A(–4, 3), B(2, 3), C(–1, –2), and D(–7, –2)

HOMEWORK

Practice WS on Parallelograms

Find the value of each variable.1. 2.

R

U

S

T

2a

3a - 5

b + 32b - 1


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3. 4.Find the value of each variable.5. 6.

Use „RSTU to find each measure or value.

7. m⁄RST = _____

8. m⁄STU = _____

9. m⁄TUR = _____

10. b = ______

Coordinate Geometry. Find the coordinates of the intersection of the diagonal of „HJKL with the given vertices.

11. H(1, 1), J(2, 3), K(6, 3), L(5, 1)


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Coordinate Geometry. Find the coordinates of the intersection of the diagonal of „HJKL with the given vertices.

12. H(–1, 4), J(3, 3), K(3, –2), L(–1, –1)

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 m⁄1 is 130, find m⁄2, m⁄3, and m⁄4.

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?

Find the value of each variable.15. 16.


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17. 18.Answers:

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. m⁄2 = 50, m⁄3 = 130, m⁄4 = 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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6.2 parallelograms 2016 ink.notebook€¦ · 6.2 parallelograms 2016 ink.notebook 1 January 11, 2017 Page 15 6.2 Parallelograms Don't forget to put it in the table of contents Page