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Unit 1: Tools of Geometry
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last edited
by Christine Koerner 4 years, 2 months ago
Big Idea 1: Undefined terms and congruence are the cornerstones of geometry.
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Lessons and Additional Activities
Big Idea 1 Lessons 1-4 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Identify the difference between congruence and incongruence.
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Given any two objects (non-geometric), describe what is the same and different about them
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Identify and justify why two objects are the same or different
- Discuss the difference between points, lines, rays, and line segments (undefined terms) in terms of congruence
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Demonstrate how a straight line segment can be drawn joining any two points (Euclid’s first postulate)
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Demonstrate how any straight line segment can be extended indefinitely in a straight line (Euclid’s second postulate)
Justify which qualities are significant or insignificant for determining if two segments in geometry are congruent
Construct congruent segments and justify their congruence
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Given a line segment, create a congruent segment, and explain why they are congruent
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Bisect a line segment and justify congruence of both parts
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Compare methods for determining congruence and describe advantages of each type
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Examples: paper folding, placing the segment (vertical and horizontal only) on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.
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Big Idea 2: Congruent angles have equal angle measure.
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Lessons and Additional Activities
Big Idea 2 Lessons 1-3 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Describe qualities that make two angles congruent or incongruent
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Define an angle using its vertex and rays
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Define all straight angles as having 180° and are therefore all congruent angle measures
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Justify which qualities are mathematically significant or insignificant for determining if two angles are the same
Construct congruent angles and justify their congruence
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Compare methods for determining congruence and describe advantages of each type
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Examples: paper folding, placing angles on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.
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Given an angle, create a congruent angle, and explain why they are congruent
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Bisect an angle and justify congruence of both parts
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Perform constructions and analyze the relationships among the segments or angles created
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Big Idea 3: Line segment relationships are determined by length and direction on the coordinate plane.
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Lessons and Additional Activities
Big Idea 3 Lessons 1-3 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Analyze distance in the coordinate plane and use distance to relate points and lines
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Calculate the distance between two points using the Pythagorean Theorem
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Generalize methods for determining the distance between two coordinate points
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Explain how the distance formula can be used to find length measurements of segments (or sides of a geometric figure)
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Find the coordinates of a segment’s midpoint
Describe direction in the coordinate plane and use direction to relate points and lines
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Generalize methods for determining the direction between two coordinate points
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Identify and justify if two lines are parallel or perpendicular
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Create equations that represent parallel lines or perpendicular lines
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Unit 1: Tools of Geometry
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