Download Geometry

Mathematics Instructional Design
Lesson Planning Template
Class: Geometry
Lesson: 4.2
Date: 2016
Important Mathematics to Develop
In Critical Area 1: Congruence with Transformations, students complete constructions to visually represent geometric
theorems. Specifically in Lesson 4.2, students inductively conjecture that the base angles of an isosceles triangle are
congruent (the Isosceles Triangle Conjecture), and the Converse of the Isosceles Triangle Conjecture.
Standards for Mathematical Practice and Content
G-CO.C.10: Prove theorems about triangles.
G-CO.D.12: Make formal geometric constructions with a variety of tools and methods.
SMP.3: Construct viable arguments and critique the reasoning of others.
SMP.5: Use appropriate tools strategically.
Learning Intention
We are learning to discover properties of isosceles triangles.
Success Criteria
We are successful when we can articulate the relationship between the base angles of an isosceles triangle.
Mathematical Task and needed material
Additional notes
Discovering Geometry Lesson 4.2
Vocabulary:
Base Angles
Vertex Angle
Base
Leg
Isosceles Triangle
Converse
Patty Paper
Protractors
Compasses
Straight Edges
Page 1 of 2
June 2016
Launch
5 minutes
Listen to students’
background knowledge with
the vocabulary words that
they will encounter
throughout the lesson. After
each round have students
share how their partners
successfully described each
term.
Talk-A-Mile-A-Minute
Round 1: Side, Angle, Triangle, Congruent, Base
Round 2: Isosceles, Leg, Vertex Angle, Base Angles, Converse
Explore
Notes/reflection
20-25 minutes
Small Group: 10 minutes
Investigation 1: Base Angles in an Isosceles Triangle
 Arrange students in groups of four.
 Have students work with a partner to complete the investigation. Be sure that one
partnership in the group uses an acute angle, and the other partnership uses an
obtuse angle.
 Have the group compare the results from the two different triangles and complete
the conjecture.
Whole Group: 5 minutes
Discuss how the Isosceles Triangle Conjecture applies to equilateral triangles.
See pp. 206-211 for details.
Small Group: 10 minutes
Investigation 2: Is the Converse True?
 Again have students work in their groups of four.
 Have students work with a partner to complete the investigation. Be sure each
partnership starts with different angles.
 Have the group compare the results from the two different triangles and complete
the conjecture.
Summarize
5-10 minutes
Have students discuss the Isosceles Triangle Conjecture and the Converse of the Isosceles
Triangle Conjecture, making sure students articulate the relationship between the base
angles of an isosceles triangle.
Also discuss with students the idea that a converse of a true conjecture need not be true,
but if it is, the two can be combined into a bi-conditional “if and only if” statement.
Apply
Have students work in small groups to complete question 11 on page 209.
See pp. 206-211 for details.
Homework: Exercises 1-10
5-10 minutes
See pp. 206-211 for details.
Page 2 of 2
June 2016