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 hand2mind Join our community on edWeb.net Building Understanding in Mathematics www.edweb.net/math

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

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Building Understanding in Mathematics Join our community on edWeb.net Building Understanding in Mathematics Invitations to upcoming webinars Webinar recordings and resources CE quizzes 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 hand2mind 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? No Yes

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 AngLegs 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 Not Right Triangles Right Triangles

Classifying Triangles Is the largest angle acute? No Yes Not Right, Not Acute Triangles Acute Triangles 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. 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 CE Certificate provided by

Join us for the next webinar Tuesday, December 1st 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 hand2mind For an invitation to the next webinar join Building Understanding in Mathematics www.edweb.net/math

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