Deductive Reasoning
Lesson Plan 013
Class: Geometry Date: Friday October 23rd/Monday October 26th, 2020
Topic: Deductive Reasoning in Geometry Aim: How do we use deductive reasoning to prove statements in geometry?
HW # 013: Page 4 of this lesson
Do Now:
We stated that a triangle that has two congruent sides is an isosceles triangle. Using your compass and straight-edge, construct two different isosceles triangles
First Isosceles Triangle Second Isosceles Triangle
In each isosceles triangle, use a protractor to measure the base angles. Based on this exercise, what can you state about the base angles of an isosceles triangle?
PROCEDURE:
Write the Aim and Do Now Assignment #1: Let’s go to and
Get students working! take a look at isosceles triangles and their base
Take attendance angle measures.
Give Back HW
Collect HW
Go over the Do Now
In the Do Now, we looked at some examples and then made a general truth based on those examples. That type of reasoning is called inductive reasoning. Use inductive reasoning to find the next term in the pattern
Inductive reasoning is good, but it has its drawbacks.
With inductive reasoning, you are making conclusions without examining every possible example. Any single counterexample is sufficient to show that a general conclusion reached is false.
Assignment #1:
For example, if I measured all the angles of many isosceles triangles and found that all the angles I measured are acute angles, I would conjecture that all angles of isosceles triangles are acute. Can you show a counter example to show my conclusion is false?
Assignment #2:
1)
2)
3)
Instead of using inductive reasoning, if we instead use definitions, laws, rules, formulas, theorems and other statements assumed to be true (postulates) to arrive at a true conclusion, then we are using deductive reasoning. For example,
Which Law was used to arrive at the above true conclusion?
Assignment #3: Determine if the following examples of reasoning are inductive or deductive.
Assignment #4:
Assignment #5:
Example #1: A demonstration of proving a statement using deductive reasoning.
For example,
Given: M is the midpoint of [pic]
Prove: AM=BM
|Statements |Reasons |
|M is the midpoint of [pic] |Given |
| |A midpoint divides a line segment into 2 congruent segments. (1) |
|[pic] | |
In the proof above, the premises of the argument must be taken as true statements. In geometry, there are statements that are made that are neither undefined terms (such as point, line) nor definitions (a triangle is a polygon that has exactly 3 sides).
Definition: A postulate is
Definition: A theorem is
Let’s examine some postulates and see how they are used in proofs.
The following 3 equality postulates are also referred to as the properties of equality.
The Reflexive Property of Equality
[pic] A quantity is equal to itself
The Symmetric Property of Equality
If [pic], then [pic]
The Transitive Property of Equality
If [pic]and [pic], then [pic]
HW#13 Name ____________________________________ Per _____________ Date ____________
Write proofs indicated below:
1.
|Statements |Reasons |
|1.CD = 2 inches |1. Given |
|2. XY= 2 inches |2. |
|3. |3.Transitive Property of Equality (1,2) |
| | |
| | |
Do proofs 2 and 3 below.
-----------------------
Objectives:
1) Students will be able to prove statements using the reflexive, symmetric and transitive properties of equality.
is an example of deductive reasoning!
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