Download Instructor: Qian Bradley - Disciplinary

Instructor:
Qian Bradley
Subject:
Properties of Isosceles Triangle (Geometry)
Content Goal:
1. Review the definition and vocabularies of the
isosceles triangle:
a. an isosceles triangle is a triangle with at
least two congruent sides
b. a triangle with at least two congruent sides
is an isosceles triangle
2. Isosceles triangle conjecture: if a triangle is an
isosceles triangle, then the base angles are
congruent
3. Converse of the isosceles triangle conjecture: if a
triangle has 2 congruent angles, then it is an
isosceles triangle.
Literacy Focus:
Mathematic vocabularies and responsive teaching in a
Three-Part Learning Framework
a. Pre-learning, review vocabularies with the
students:
i. isosceles triangle
ii. equilateral triangle
iii. congruent
iv. conjecture
v. converse
b. During-learning, use the text book, visual helper
and study guide, do group reading and assessment
of new vocabularies:
i. vertex angle
ii. base
iii. base angle
iv. leg
v. base triangle conjecture
vi. converse of the base triangle conjecture
c. After-learning, use the triangle-square-circle
method, let the students write reflective notes
AZ State Standards:
1. MHS-S4C1-06 Solve
relationships and
2. MHS-S4C1-10 Solve
including special
problems using angle and side length
attributes of polygons.
problems using right triangles,
triangles.
3. MHS-S5C2-02. Solve problems by formulating one or more
strategies, applying the strategies, verifying the
solution(s), and communicating the reasoning used to
obtain the solution(s).
Prerequisites:
Understanding of the isosceles triangle definition
(Chapter 1)
Instructional Objectives:
Objectives
1. Review the definition of
the isosceles triangle and
the related vocabularies.
2. Solve problems related to
the conjecture of the
isosceles triangle and its
converse.
Assessment
In class activity
Group activity: study guide
questionnaire
Individual work: worksheet
Instructional Procedure:

Warm up: Review the definition and vocabularies of
isosceles triangle
Questions to ask:
Rhetorical: Anyone remember what is an isosceles
triangle?
Review
i.
ii.
iii.
iv.
v.
the following vocabulary with the students:
isosceles triangle
equilateral triangle
congruent
conjecture
converse
Question to ask:
Rhetorical: Is equilateral triangle an isosceles
triangle?

Anticipatory hook:
Euclid (Greek mathematician
popularly considered as the
He is believed to have been
during the reign of Ptolemy
from 300 BC.), is
"Father of Geometry".
active in Alexandria,
I (323 BC–283 BC).
Euclid’s Element Book I Proposition 5 stated a
conjecture - In an isosceles triangle the angles at the base are
equal. Pappus (Greek) who followed him gave a clever
proof of this theorem.

Transition: distribute the visual helper and study
guide. Group students with 3 – 4 students per group.
Ask the students to make sure work on the questions
on the handout using their text books.

Group work: Read text book (Geometry) chapter 4.2,
using the visual helper and study guide handout.
(-Handout:
i.
ii.
iii.
iv.
v.
vi.
What is vertex angle of an isosceles
triangle?
What is the base of an isosceles triangle?
What is the base angle of an isosceles
triangle?
What is the leg of an isosceles triangle?
What is the isosceles triangle base
triangle conjecture?
What is the isosceles triangle converse of
the base triangle conjecture?
--)

Discussion:
Each group will take turns answer the questions in
the study guide. Class as a whole, check the answers
and make sure students correct the definition of the
vocabularies.
Transition: students return to their original
seating. Distribute worksheet.

Class Activity: Worksheet page 1
Ask the students to report on answers after each
problem. Through the assessment, decide whether to
move on or review part of the content.
1.





Mark
Mark
Find
Find
Find
the
the
the
the
the
leg(s) on the diagram
base on the diagram
value of the vertex angle
value of the base angle
value of angle “x”
2. Fill in the blanks.

Class Activity: Worksheet page 2
Ask the students to report on answers after each
problem. Through the assessment, decide whether to
move on or review part of the content.
1.


Find mPQR
Find mP


Find the value of the vertex angle
Find the value of the base angle
2. In class discussion.

Closure:
Introduction to Triangle-Square-Circle method: what
are the 3 most important things that you learned
today, what squares (clicks) with your interest in
math, what question still circles around your head?
Students do their own reflective writing: call out 2
students to read what they write and share.