Lanie chapter 6

Lanie, Oct 19, 2017

Table of Contents

  1. Corollary to the polygon angle-sum theorem
    1. Obvious Corollary
    2. Consecutive Interior Angles Theorem
    3. Effortless Trisections
    4. Diagonals in a quadrilateral
    5. Animation 35
  2. Theorem 6-2 polygon exterior angle-sum theorem
    1. Quadrilateral: Exterior Angles
    2. Shineequa´´s Regular Polygon
  3. Theorem 6-3
    1. Special Quadrilateral: Theorem 1
  4. Theorem 6-4
    1. Triangle Angle Sum Theorem
  5. Theorem 6-5
    1. Proof that Congruent Opposite Angles Implies Parallelogram
    2. Theorem 40
  6. Theorem 6-6
    1. Animation 125
    2. Parallelogram: Theorem (3)
  7. Theorem 6-7
    1. Animation 134
  8. Theorem 6-8
    1. Proof for circumscribable quadrilateral
    2. Opposite angles and Cyclic Quadrilateral
  9. Theorem 6-9
    1. Consecutive Angles (SUPPLEMENTARY)
    2. Consecutive Interior Angles (Supplementary)
  10. Theorem 6-10
    1. Parallelogram: Theorem 1
  11. Theorem 6-11
  12. Theorem 6-12
    1. parallel and congruent segment
    2. SAS - Exercise 1B
  13. Theorem 6-13
    1. Rhombus Action!
    2. ACCESS - Rhombus
  14. Theorem 6-14
    1. Construction of 5 Parallelograms
  15. Theorem 6-15
    1. Theorem 4.1.1
  16. Theorem 6-16
    1. Rhombus Diagonals
    2. Geometry Lesson 6-4 Characteristics of a Rhombus
  17. Theorem 6-17
    1. Rhombus With Bisected Angles
  18. Theorem 6-18
    1. Rectangle Diagonals
    2. Diagonals of a Rectangle
  19. Theorem 6-19
    1. Graph the Line
    2. ACCESS - Trapezoid
  20. Theorem 6-20
    1. Isosceles Trapezoid Template
  21. Theorem 6-21
    1. Dynamic Proof Of Triangle Mid-Segment Theorem
    2. Mid-segment of a Trapezoid
  22. Theorem 6-22
    1. ACCESS - Kites
    2. Kite Template: Scaffolded Investigation

1.

Corollary to the polygon angle-sum theorem

  • 1. Obvious Corollary
  • 2. Consecutive Interior Angles Theorem
  • 3. Effortless Trisections
  • 4. Diagonals in a quadrilateral
  • 5. Animation 35

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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2.

Theorem 6-2 polygon exterior angle-sum theorem

  • 1. Quadrilateral: Exterior Angles
  • 2. Shineequa´´s Regular Polygon

2.1.

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2.2.

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3.

Theorem 6-3

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

  • 1. Special Quadrilateral: Theorem 1

3.1.

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4.

Theorem 6-4

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

  • 1. Triangle Angle Sum Theorem

4.1.

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5.

Theorem 6-5

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

  • 1. Proof that Congruent Opposite Angles Implies Parallelogram
  • 2. Theorem 40

5.1.

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5.2.

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6.

Theorem 6-6

If a quadrilateral is a parallelogram, then its diagonal bisect each other.

  • 1. Animation 125
  • 2. Parallelogram: Theorem (3)

6.1.

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6.2.

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7.

Theorem 6-7

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruents on every transversal.

  • 1. Animation 134

7.1.

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8.

Theorem 6-8

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  • 1. Proof for circumscribable quadrilateral
  • 2. Opposite angles and Cyclic Quadrilateral

8.1.

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8.2.

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9.

Theorem 6-9

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

  • 1. Consecutive Angles (SUPPLEMENTARY)
  • 2. Consecutive Interior Angles (Supplementary)

9.1.

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9.2.

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10.

Theorem 6-10

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  • 1. Parallelogram: Theorem 1

10.1.

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11.

Theorem 6-11

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.


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12.

Theorem 6-12

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

  • 1. parallel and congruent segment
  • 2. SAS - Exercise 1B

12.1.

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12.2.

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13.

Theorem 6-13

If a parallelogram is a rhombus, then it's diagonals are perpendicular.

  • 1. Rhombus Action!
  • 2. ACCESS - Rhombus

13.1.

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13.2.

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14.

Theorem 6-14

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

  • 1. Construction of 5 Parallelograms

14.1.

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15.

Theorem 6-15

If a parallelogram is a rectangle, then it's diagonals are congruent.

  • 1. Theorem 4.1.1

15.1.

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16.

Theorem 6-16

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rombus.

  • 1. Rhombus Diagonals
  • 2. Geometry Lesson 6-4 Characteristics of a Rhombus

16.1.

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16.2.

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17.

Theorem 6-17

If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

  • 1. Rhombus With Bisected Angles

17.1.

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18.

Theorem 6-18

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

  • 1. Rectangle Diagonals
  • 2. Diagonals of a Rectangle

18.1.

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18.2.

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19.

Theorem 6-19

If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.

  • 1. Graph the Line
  • 2. ACCESS - Trapezoid

19.1.

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19.2.

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20.

Theorem 6-20

If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

  • 1. Isosceles Trapezoid Template

20.1.

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21.

Theorem 6-21

If a quadrilateral is a trapezoid then, (1)the midsegement is parallel to the bases, and (2)the length of the midsegment is half the sum of the lengths of the bases.

  • 1. Dynamic Proof Of Triangle Mid-Segment Theorem
  • 2. Mid-segment of a Trapezoid

21.1.

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21.2.

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22.

Theorem 6-22

If a quadrilateral is a kite, then its diagonals are perpendicular.

  • 1. ACCESS - Kites
  • 2. Kite Template: Scaffolded Investigation

22.1.

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22.2.

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