Download Angle Properties

Angle Properties of 2D Shapes: Teacher Notes
Overview
In this activity students explore and use angle properties of 2D shapes.
Important Mathematical Ideas
 Shapes have properties that can be analysed and help to explain the world around
us.
 Understanding the geometric properties of shapes helps you to solve real-world
problems.
Prior Knowledge
 Identifying types of angles (e.g., obtuse, right, acute).
 Identifying types of triangles (e.g., obtuse, right, acute, isosceles, equilateral,
scalene).
 Applying angle properties of intersecting lines (e.g., supplementary angles,
complementary angles, vertically opposite angles) to determine angle measures.
 Applying angle properties of triangles (e.g., angle sum, isosceles triangle, equilateral
triangle) to determine angle measures.
Common Misconceptions
 Applying properties of parallel lines to lines that are not parallel.
 Interchanging supplementary and complementary angles.
Information to Support/ Enhance/ Extend Learning
 Students are asked to keep a journal for each unit in the course. It should contain
notes of important mathematical ideas with examples and new vocabulary.
 ePortfolio may be used for these journal entries.
 Students can make individual choices whether this is a paper or digital personal
resource.
 Consider a variety of formats as alternatives to journal entries (e.g., student note,
pair/share, group discussion, exit card, poster, electronic posting).
 Develop a Word Wall and continue it throughout the unit as new vocabulary and
terms arise that require clarification (e.g., obtuse angle, right angle, acute angle,
triangle, supplementary angles, complementary angles, vertically opposite angles,
exterior angle, equilateral triangle, isosceles triangle, scalene triangle, obtuse
triangle, acute triangle).
Minds On
Task 1: Geometry in Real-Life Video and Journal Prompt and Sample Response
Watch the video and record three geometric properties that you found interesting.
Grade 9 Applied Blended Learning: Unit 8 Activity 1
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Angle Properties of 2D Shapes: Teacher Notes
1. Railway Tracks form parallel lines.
2. Two-dimensional shapes, like octagons, hexagons and squares, can be seen in
patio stones.
3. Angles can be found in nature.
Task 2: Types of Triangles
Students will:
 visit the website Interactive Triangles to explore properties of triangles
 complete a worksheet to define six types of triangles: equilateral, isosceles,
scalene, acute, right and obtuse
Discussion Prompt and Sample Responses
Describe how your definitions and examples are similar or different.
 Solutions should include:
o definitions of types of triangles
o a picture, or sketch, of a real-life example for each type of triangles
 Common Errors:
o confusion of the types of triangles
o no or incorrect real-life example given
 Students' examples of types of triangles may be shared through a Gallery Walk.
 To provide a visual cue for Types of Triangles consider co-developing an Anchor
Chart.
Grade 9 Applied Blended Learning: Unit 8 Activity 1
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Angle Properties of 2D Shapes: Teacher Notes
Action
Task 3: Getting Familiar with Geometer's Sketchpad
 GSP Intro Video
o This intro to GSP can be done as a whole class with the teacher demonstrating the

various tools that may be used. It will be important for the students to work with the
tools before attempting any of the activities.
Students will use GSP Intro Sketch and reference guide to:
o explore the tools and menus in GSP
o construct a triangle
o create and measure an angle
o create a triangle and find the sum of angles of their triangle
Task 4: Investigating Angle Properties
 Students will use Angle Properties GSP Sketch to
o investigate the properties of angles (supplementary, complementary, opposite)
and provided real-world examples
o investigate the angles in a triangle (isosceles, equilateral, exterior and sum)
o complete Angle Properties worksheet
Check Your Understanding
Students will:
 solve angle properties problems
 check with provided solutions
Task 5: Exploring Geometry in Real-Life with GSP
 Geometer's Sketchpad 5: Working with Pictures video
o Video demonstration on how to import pictures into GSP
 Students will:
o investigate the angle properties of the triangular trusses of the Worcester
Railway Bridge using GSP (a pre-made sketch is provided if students choose
not to insert the picture)
o confirm or deny that the triangular trusses are equilateral triangles
o compare their solution with the Worchester Railway Solution video provided
Consolidation
Task 6: Angles in a Triangle Practice Quiz
 Interactive Quiz to review angle properties.
o sample solutions provided
 Students can take a screenshot of their work.
 Students can do this practice exercise in pairs.
 The Angles in A Triangle Quiz can be done as a whole-class activity with the
students using clickers to give their answers or as a paper and pencil quiz.
Grade 9 Applied Blended Learning: Unit 8 Activity 1
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Angle Properties of 2D Shapes: Teacher Notes
Task 7: Assignment 1: What's My Angle?
 Posted with unit.
 See sample solution in the Teacher Notes posted on the Virtual Learning.
Environment (vLE).
Task 8: Assignment 2: Is the Portico Isosceles?
 Posted with unit.
 See sample solution in the Teacher Notes posted on the Virtual Learning.
Environment (vLE).
Task 9: Student Reflection
 Students are asked to reflect on their understanding of this topic.
 These reflections can be used as assessment for learning to help determine next
steps for individual students.
Grade 9 Applied Blended Learning: Unit 8 Activity 1
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