1. Chelsea Prue
Introduction to Triangles and Logic (Unit Organizer)
Introduction
• Lesson Topic: Introduction to Triangles and Logic (Unit Organizer).
• Length of Lesson: 90 minutes (1 block)
• VA Standards of Learning:
• G.1 The student will construct and judge the validity of a logical argument consisting of a set of
premises and a conclusion. This will include
a. identifying the converse, inverse, and contrapositive of a conditional statement.
b. translating a short verbal argument into symbolic form.
c. using Venn diagrams to represent set relationships; and
d. using deductive reasoning, including the law of syllogism.
 G.5 The student will
a. investigate and identify congruence and similarity relationships between triangles; and
b. prove two triangles are congruent or similar, given information in the form of a figure or
statement, using algebraic and coordinate as well as deductive proofs.
 G.6 The student, given information concerning the lengths of sides and/or measures of angles will
apply the triangle inequality properties to determine whether a triangle exists and to order sides and
angles. These concepts will be considered in the context of practical situations.
 G.7 The student will solve practical problems involving right triangles by using the Pythagorean
Theorem, properties of special right triangles, and right triangle trigonometry. Solutions will be
expressed in radical form or as decimal approximations.
Cognitive Objectives
Students will:
• Identify the converse, inverse, and contrapositive of a conditional statement.
• Translate short verbal arguments into symbolic form, such as (pq) and (~p~q).
• Use and interpret Venn diagrams.
• Determine the validity of a logical argument.
• Use valid forms of deductive reasoning, including the law of syllogism.
• Select and use various types of reasoning and methods of proof, as appropriate.
• Use definitions, postulates, and theorems to determine whether triangles are congruent/similar.
• Use algebraic methods, such as properties of proportions, to prove that triangles are similar.
• Use coordinate methods, such as the distance formula, and the slope formula, to prove two triangles are
congruent.
• Given the lengths of three segments, determine whether a triangle could be formed.
• Arrange the angles of a triangle in order from smallest to largest when given the lengths of the sides.
• Arrange the sides of a triangle in order from smallest to largest when given the measures of the angles.
• given the lengths of two sides of a triangle, determine the range in which the length of the third side must
lie.
• Given the lengths of two sides of a right triangle, use the Pythagorean Theorem to find the length of the
third side.
• Determine whether a triangle formed with three given lengths is a right triangle.
• Solve for missing lengths in geometric figures, using properties of 45°-45°-90° triangles, and 30°-60°-90°
triangles.
• Solve problems involving right triangles, using sine, cosine, and tangent ratios.
• Solve practical problems, using right triangle trigonometry and properties of right triangles.
Materials/Technology and Advanced Preparation
• Smartboard/projector for powerpoint.
• Blank Unit Organizer handout for each student.
Teaching and Learning Sequence
Introduction/Anticipatory Set
1

2. Chelsea Prue
Introduction to Triangles and Logic (Unit Organizer)
• Factstorming: Have each student write down at least three facts that they already know about triangles or
logical arguments.
• Hand out blank Unit Organizer to each student.
Lesson Development
• Explain each section of the Unit Organizer, while students fill in their own copy. Be sure to emphasize the
due dates on the left side in the Unit Calendar.
Closure
• Students write one sentence about how the current unit, Triangles and Logic, relates to the previous unit,
Lines and Angles.
• Students write down one sentence about how the current unit, Triangles and Logic, relates to the next unit,
Polygons and Circles.
Homework
- Read Textbook pg. 145-155
- Textbook pg. 156, # 1-10.
Assessment
Formative
• Students relate current material to previous and following material.
Summative
• Students complete a homework assignment that reflects their ability to read and understand the text.
2

3. Chelsea Prue
Introduction to Triangles and Logic (Unit Organizer)
Instructional Content and Strategies Organizer
Instructional Content
- See attached Unit Organizer.
Instructional Modifications to ASSIST
Weakest Students
Major Instructional Strategies
Instructional Modifications to CHALLENGE
Strongest Students
- Students copy information onto their own
unit organizer from the projector screen.
- Students keep all information organized in
one place on the unit organizer.
- Students keep all information organized
in one place on the unit organizer.
- Students see a detailed Unit calendar as
part of the unit organizer.
- Students answer Unit Self-Test questions
from the previous and current unit.
3