8.G.1Verify experimentally the properties of rotations, reflections, and translations:
A. Lines are taken to lines, and line segments to line segments of the same length. B. Angles are taken to angles of the same measure. C. Parallel lines are taken to parallel lines. |
8.G.2Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
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8.G.3Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles
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Conceptual Understanding
Imagine yourself waking up in the morning, opening the door to the bathroom, squinting your eyes in the light, walking across your tiled floor, taking a look in the mirror, and sliding the toothpaste across the counter after you put some on your toothbrush. Sounds like just another typical start to your morning, but, in the world of mathematics, you just encountered several geometric transformations.
Perhaps a mathematician would recap their morning as ROTATING the door to the bathroom, DILATING their eyes to adjust to the amount of light, walking across their TESSELLATED tile floor, taking a look at their REFLECTION, and TRANSLATING their toothpaste across the counter.
There are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage.
Perhaps a mathematician would recap their morning as ROTATING the door to the bathroom, DILATING their eyes to adjust to the amount of light, walking across their TESSELLATED tile floor, taking a look at their REFLECTION, and TRANSLATING their toothpaste across the counter.
There are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage.
Rigid Transformations Lesson:
Translations
A translation is a "push" or a "slide". The orange original triangle has been pushed 6 units to the right. Later we will calculate the shift by tracking the coordinates of the original and the image.
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Reflections
A reflection is a "flip" over a given "line of reflection". In this example the orange original triangle has been flipped over the y-axis (line of reflection) resulting in the blue triangle or image of the original.
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Rotations
A rotation is a "spin" or a "turn" about a "center of rotation". Typically the center of rotation is the origin. The orange original triangle has been rotated about the origin 180 degrees to the blue image of the original.
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Rigid Transformation Practice:
Translations #138151 Reflections # 647139 Rotations # 818626 |
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Time to Show what you Know
Non-rigid Transformations Lesson
A non-rigid transformation is a transformation that changes the size of a figure but not the shape. We will study dilations in our unit.
What is a dilation?
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Non-Rigid Transformation Practice
DILATIONS # 844159 |
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Time to Show what you Know
TRANSVERSAL LESSON:
TIP: An easy way to remember the measure of angles is demonstrated by the graphs below. Angles are divided into two groups - small and large. All the small angles are the SAME!! All the large angles are the SAME!! One small plus one large equal 180 degrees and form a straight line.
Another handy tip: All triangles have a total of 180 degrees. This is a helpful definition when determining unknowns.
Use the above charts to complete transversal practice #1
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Transversal Practice:
Angle Measures Challenge #1
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Angle Measures using Triangles Challenge #2
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