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.
4. Apply algebra to angle properties
Literacy Focus:
Math vocabulary and responsive teaching in a ThreePart Learning Framework
a. Pre-learning, review vocabularies with the
students:
i. isosceles triangle
ii. vertex angle
iii. base
iv. base angle
v. leg
vi. equilateral triangle
vii. congruent
viii. conjecture
ix. converse
b. During-learning, assess students vocabularies
through in-class activities
c. After-learning, use the triangle-square-circle
method, let the students write in their notes
AZ State Standards:
1. MHS-S4C1-06 Solve problems using angle and side length
relationships and attributes of polygons.
2. MHS-S4C1-10 Solve problems using right triangles,
including special 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:
1. Understanding of the isosceles triangle definition
(Chapter 1)
2. Understanding of Algebra
Instructional Objectives:
Objectives
1. Review/reflect the
definition of the isosceles
triangle and the related
vocabularies.
2. Solve problems related to
the conjecture of the
isosceles triangle and its
converse.
3. Apply algebra to angle
properties
Assessment
In class discussion
In class activity: worksheet
In class discussion
In class activity: 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/reflect from Chapter 1 that an isosceles
triangle is a triangle with at least two congruent
sides. In an isosceles triangle, the angle between
the two congruent sides is called the vertex
angle, and the other two angles are called the base
angles. The side between the two base angles is
called the base of the isosceles triangle. The other
two sides are called the legs.
Question to ask:
Rhetorical: Is equilateral triangle an isosceles
triangle?

Anticipatory hook:
Euclid (Greek mathematician from 300 BC.), is
popularly considered as the "Father of Geometry".
He is believed to have been active in Alexandria,
during the reign of Ptolemy 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 worksheet
Ask the students to make sure look at the worksheet
page 1.
Question to ask:
Managerial: Everyone with me on page 1 of the
worksheet?

Lecture:
The isosceles triangle conjecture: If a triangle is
isosceles, then base angle are congruent.
Example:
Find the missing angle “x”

Class Activity: Worksheet page 1
1. Ask the students to think about the 1st problem,
get their initial thoughts. Then model the
solution.
2. Ask the students to work on the 2nd problem. Ask
for student volunteers.

Lecture:
Converse of the isosceles triangle conjecture:
If a triangle has 2 congruent angles or 2 congruent
sides, then it is an isosceles triangle.
Example:

Class Activity: Worksheet page 2
1. In class discussion.
2. Ask the students to think about the 2nd problem,
get their initial thoughts. Then model the
solution.

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.