EdPower
Shah, Ronak / Geometry (M) / Grade 9 (Tindley Accelerated School)
Tuesday, June 25, 2013, 8:29AM /
Unit: Unit 3: Triangles(Week 8, 3 Weeks)
Taught Curriculum
Stage 1 - Desired Results
Established Goals
IN: CCSS: Mathematics, IN: HS: Geometry, Congruence
G-CO Prove geometric theorems
- 10. Prove theorems about triangles.
- 12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
- 13. Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.
G-C Understand and apply theorems about circles
- 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G-MG Apply geometric concepts in modeling situations
- 1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★
Key Words/Vocabulary
Proof: A set of rigorous reasoning that guarantees the truth or falsehood of a statement.
Triangle: A polygon with three vertices and three edges.
Equilateral: A shape where all sides are line segments of equal length.
Isosceles: A triangle where two legs are line segments of equal length.
Interior Angles: The measures of the angles on the inside of a shape.
Base Angles: The angles directly adjacent to the base of a shape.
Midpoint: The point that divides a line segment into two congruent halves.
Median: The line segment joining a vertex to the midpoint of the opposite side.
Altitude: The line segment perpendicular to the base of a triangle.
Circumscribe: To draw a circle that passes through all the vertices of a polygon.
Inscribe: To draw a circle that passes through all the edges of a polygon.
Essential Questions
When a vertex, side, or angle is changed in a triangle, how is the triangle affected?
What is the relationship between a triangle and more complex shapes?
How can properties of triangles be modeled with real-world objects? / Understandings
Students will understand…
- The circle inscribed in a polygon will always be smaller than that which circumscribes it.
- If the smaller sides of a triangle sum to the larger side, the triangle degenerates to a line.
- The properties of the sides of a triangle allow us to prove statements about its angles.
- The properties of the angles of a triangle allow us to prove statements about its sides.
- Because mathematics is a logical system, we can prove statements indirectly by assuming the opposite and creating a contradiction.
Key Knowledge
Students will know that…
- The measures of the interior angles of a triangle sum to 180 degrees.
- The base angles of an isosceles triangle are congruent to each other.
- A bisector separates a line segment into two congruent line segments and an angle into two congruent angles.
- A perpendicular bisector separates a straight angle into two congruent right angles.
- The medians of a triangle meet at a point.
- The bisectors of a triangle meet at a point.
Students will be able to…
- Use tools to construct equilateral triangles and inscribed and circumscribed circles.
- Use a straightedge, protractor, and compass to copy and bisect angles and line segments.
- Identify patterns and make inductive conjectures about the properties of triangles.
- Use a proof to support a logical argument and prove a theorem about triangles.
- Prove a theorem using an indirect proof.
Stage 2 - Assessment Evidence
Evidence of Student Understanding
Unit 3 Test -- Triangles
Summative:Test: Standardized
Unit 3 Test and Key.pdf
Stage 3 - Learning Plan
Detailed Unit Plan
Unit 3 Calendar - Triangles.docx / Learning Ladder / Lesson Plan
Syllabi
Attach your syllabi with Links
Resources / Unit Reflection
Last Updated: Tuesday, June 25, 2013, 8:28AM
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