Geometric Reasoning with Shapes Attributes Part 3 Properties

Geometric Reasoning with Shapes & Attributes Part 3: Properties of Lines and Angles Tuesday, November 10, 2015 Presented by Sara Delano Moore, Ph. D. Director of Mathematics and Science at ETA hand 2 mind Join our community on ed. Web. net Building Understanding in Mathematics www. edweb. net/math

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Join our community on ed. Web. net Building Understanding in Mathematics ü Invitations to upcoming webinars ü Webinar recordings and resources ü CE quizzes ü Online discussions Join the community www. edweb. net/math

Geometric Reasoning with Shapes & Attributes Properties of Lines and Angles Sara Delano Moore, Ph. D. Director of Mathematics & Science ETA hand 2 mind 10 November 2015

Geometric Reasoning with Shapes & Attributes • • September 15: Laying a Strong Foundation October 13: Identifying Critical Attributes November 10: Properties of Lines and Angles December 1: Classifying Plane Figures

Levels of Geometric Understanding • Level 0: Visualization – “It looks like …” – Focus only on the shapes available at the time • Level 1: Analysis – “Laundry list” of properties – Understanding of classes of shapes with common properties • Level 2: Informal Deduction – Identify informal relationships among properties – Identify necessary and sufficient properties • Level 3: Deduction – Create proofs about properties • Level 4: Rigor – Reason about different axiomatic systems (e. g. , spherical geometry)

Properties of Lines • We call this a line segment. How does each of these words fit this object? • What would it take to make this a line? • What do we call one location on a line? – This is called a point. • What if the line started at the point? – This is called a ray.

Parallel Lines What is the relationship between these line segments?

Parallel Lines in Quadrilaterals

Perpendicular Lines What is the relationship between these line segments?

Perpendicular Lines in Polygons

Classification based on lines • Does the shape have at least one pair of parallel sides? Yes No

Classification based on lines • Does the shape have exactly one pair of parallel sides? No Yes Trapezoids Parallelograms

What is an angle? • Two rays with a common endpoint – Ang. Legs picture angles built with line segments. • Motion for angles is rotation. • Orientation of an angle does not matter – Angle size is the rotation from one ray to the next. 45° 0°

Types of Angles • What everyday objects can serve as a benchmark for right angles? – Acute angles (less than 90 degrees) – Right angle (90 degrees) – Obtuse angles (between 90 and 180 degrees) – Straight angle (180 degrees) – Reflex angles (between 180 and 360 degrees)

Measuring Angles 60°

Estimating & Measuring Angle Size 60° How does the angle compare to a right angle? 120° How does the angle compare to a straight angle?

Classifying Triangles • Is the largest angle a right angle? No Yes Right Triangles Not Right Triangles

Classifying Triangles • Is the largest angle acute? No Yes Acute Triangles Not Right, Not Acute Obtuse Triangles

Geometric Reasoning with Shapes & Attributes • • September 15: Laying a Strong Foundation October 13: Identifying Critical Attributes November 10: Properties of Lines and Angles December 1: Classifying Plane Figures

Recognition for your participation today! Attending Live? Your CE Certificate will be emailed to you within 24 hours. CE Certificate provided by Viewing the Recording? Join the community at www. edweb. net/math Go to the Webinar Archives folder Take the CE Quiz to get a personalized CE Certificate

Join us for the next webinar Tuesday, December 1 st at 4 pm (Eastern Time) Geometric Reasoning with Shapes & Attributes Part 4: Classifying Plane Figures Presented by Sara Delano Moore, Ph. D. Director of Mathematics and Science at ETA hand 2 mind For an invitation to the next webinar join Building Understanding in Mathematics www. edweb. net/math

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