1. 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
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Building Understanding in Mathematics

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5. Building Understanding in Mathematics
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6. Geometric Reasoning with Shapes & Attributes
Properties of Lines and Angles
Sara Delano Moore, Ph.D.
Director of Mathematics & Science
ETA hand2mind
10 November 2015

7. 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

8. 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)

9. 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.

10. Parallel Lines
What is the relationship between these line segments?

11. Parallel Lines in Quadrilaterals

12. Perpendicular Lines
What is the relationship between these line segments?

13. Perpendicular Lines in Polygons

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

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

16. 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°

17. 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)

18. Measuring Angles
60°

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

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

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

22. 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

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

25. 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

26. Thank you!