Cienna's chapter 6

ciennac20, Oct 17, 2017

Table of Contents

  1. 6-1
    1. Exploring Polygon Angles: Triangle through Octagon
    2. convex vs concave polygon
    3. Geometry Lesson 6-4 Characteristics of a Rhombus
    4. Congruence Shortcuts
  2. 6-2
    1. Quadrilateral With Opposite Angles Congruent
    2. Animation 186
  3. 6-3
    1. Diagonals Bisect
    2. Quadrilateral F
  4. 6-4
    1. 5.2b Diagonals of Rhombuses 1
    2. 5.2a Diagonals of Rectangles
  5. 6-5
    1. Diagonals of a Rectangle
  6. 6-6
    1. Isosceles Triangle Theorem II
  7. 6-7
    1. Distance Formula
    2. Isosceles Trapezoid Template (Scaffolded Investigation)
  8. 6-8
    1. G.CO.2 (Advanced)
    2. Triangles
    3. Midpoint Formula
  9. 6-9
    1. chapter 6 parallel
    2. chapter 6 perp.
    3. coordinates of midpoint

1.

6-1

  • 1. Exploring Polygon Angles: Triangle through Octagon
  • 2. convex vs concave polygon
  • 3. Geometry Lesson 6-4 Characteristics of a Rhombus
  • 4. Congruence Shortcuts

1.1.

Exploring Polygon Angles: Triangle through Octagon

Move the vertices (corners) of this TRIANGLE anywhere you'd like. Explore!
Move the vertices (corners) of this QUADRILATERAL anywhere you'd like. Explore!
Pentagon
Hexagon
Heptagon
Octagon
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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2.

6-2

  • 1. Quadrilateral With Opposite Angles Congruent
  • 2. Animation 186

2.1.

Quadrilateral With Opposite Angles Congruent

[color=#000000]This applet was intended to accompany the activity entitled [/color][color=#000000]What Kind of Quadrilateral is This? (Part III)[br][br][/color][i][color=#0000ff]The directions in this activity refer to this applet.  [/color][/i][color=#000000][br][br][/color][color=#000000]Teachers: To see a preview copy of this lesson activity, go to https://www.teacherspayteachers.com/Product/What-Kind-of-Quadrilateral-is-This-Part-3-of-4-2517973[/color][b][color=#000000][br][/color][br][/b]
– Tim Brzezinski

2.2.

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3.

6-3

  • 1. Diagonals Bisect
  • 2. Quadrilateral F

3.1.

Diagonals Bisect

If the diagonals of a quadrilateral bisect each other, will that quadrilateral always be a parallelogram? Click and drag the points to find out!
– Andrew Knauft

3.2.

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4.

6-4

  • 1. 5.2b Diagonals of Rhombuses 1
  • 2. 5.2a Diagonals of Rectangles

4.1.

5.2b Diagonals of Rhombuses 1

You know that the diagonals of a rhombus are perpendicular. Get a better sense of whether this is true for other parallelograms.

ABCD is currently a rhombus. Change [math]\alpha[/math] (m<DAB) to make squares and other rhombuses. Pay attention to [math]\beta[/math], the measure of the angle formed by the diagonals. Then, change the lengths of the sides to make rectangles and non-specific parallelograms. Is it still true that the diagonals have to be perpendicular? (For an obvious example, make a short (AD & BC small), long (AB & CD large) parallelogram.)
– soongy

4.2.

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5.

6-5

  • 1. Diagonals of a Rectangle

5.1.

Diagonals of a Rectangle

The figure below is a rectangle. Drag the vertices around. What do you notice about the diagonals of the rectangle?

Make a conjecture about the diagonals of a rectangle.
– Tom Maes

6.

6-6

  • 1. Isosceles Triangle Theorem II

6.1.

Isosceles Triangle Theorem II

If two angles of a triangle are congruent, then....

If two angles of a triangle are congruent, then....
– slippert12

7.

6-7

  • 1. Distance Formula
  • 2. Isosceles Trapezoid Template (Scaffolded Investigation)

7.1.

Distance Formula

Distance Formula
– David T

7.2.

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8.

6-8

  • 1. G.CO.2 (Advanced)
  • 2. Triangles
  • 3. Midpoint Formula

8.1.

G.CO.2 (Advanced)

Translation #1 Find the coordinates of the vertices of each figure after the given transformation.
Translate the given figure: translation: 4 units right and 1 unit down
Translation #2: Find the coordinates of the vertices of each figure after the given transformation.
translation: 7 units right and 1 unit down[br]A(−3, 1), B(−2, 3), C(−2, 0)
Rotation #1: Find the coordinates of the vertices of each figure after the given transformation.
rotation 90° counterclockwise about the[br]origin
Rotation #2 Find the coordinates of the vertices of each figure after the given transformation.
rotation 90° clockwise about the origin[br]B(−2, 0), C(−4, 3), Z(−3, 4), X(−1, 4)
Reflection #1: Find the coordinates of the vertices of each figure after the given transformation.
reflection across y = 2[br]A(1, 3), B(0, 5), C(1, 5), D(3, 2)
Reflection #2: Find the coordinates of the vertices of each figure after the given transformation
reflection across y = x[br]K(−5, −2), A(−4, 1), I(0, −1), J(−2, −4)
– Kirk Culler

8.2.

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8.3.

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9.

6-9

  • 1. chapter 6 parallel
  • 2. chapter 6 perp.
  • 3. coordinates of midpoint

9.1.

chapter 6 parallel

– ciennac20

9.2.

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9.3.

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