Download Geometry 15.10.23 CP1

Using Deductive Reasoning
2-3 to Verify Conjectures
Warm-Up = 2 points / +2 if you have it correct when I
come by / -2 if you’re not working on it
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
20 Point Quiz ---- Due 10/23/15
Write the converse, inverse, and contrapositive
of the conditional statement. Use the Science
Fact to find the truth value of each.
If an animal is an adult insect, then it has six
legs.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Deductive reasoning is the process of using
logic to draw conclusions from given facts,
definitions, and properties.
Deductive reasoning = conclusions from
DATA.
Inductive reasoning = conclusions from
patterns.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 1B: Media Application
Is the conclusion a result of inductive or
deductive reasoning?
There is a myth that the Great Wall of China is
the only man-made object visible from the
Moon. The Great Wall is barely visible in
photographs taken from 180 miles above Earth.
The Moon is about 237,000 miles from Earth.
Therefore, the myth cannot be true.
The conclusion is based on logical reasoning from
scientific research. It is a result of deductive
reasoning.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Determine if the conjecture is valid
Given:
If the side lengths of a triangle are 5 cm, 12
cm, and 13 cm, then the area of the triangle is
30 cm2.
The area of ∆PQR is 30 cm2.
Conjecture:
The side lengths of ∆PQR are 5cm, 12 cm, and
13 cm.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 2B: Verifying Conjectures by Using the Law
of Detachment
Determine if the conjecture is valid by the Law
of Detachment.
Given: In the World Series, if a team wins four
games, then the team wins the series. The Red
Sox won four games in the 2004 World Series.
Conjecture: The Red Sox won the 2004 World
Series.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Check It Out! Example 2
Determine if the conjecture is valid by the Law
of Detachment.
Given: If a student passes his classes, the
student is eligible to play sports. Ramon passed
his classes.
Conjecture: Ramon is eligible to play sports.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Another valid form of deductive reasoning is
the Law of Syllogism. It allows you to draw
conclusions from two conditional statements
when the conclusion of one is the hypothesis of
the other.
Law of Syllogism
If p  q and q  r are true statements, then
p  r is a true statement.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 3A: Verifying Conjectures by Using the Law
of Syllogism
Determine if the conjecture is valid by the Law
of Syllogism.
Given: If a figure is a kite, then it is a
quadrilateral. If a figure is a quadrilateral, then
it is a polygon.
Conjecture: If a figure is a kite, then it is a
polygon.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 3B: Verifying Conjectures by Using the Law
of Syllogism
Determine if the conjecture is valid by the Law
of Syllogism.
Given: If a number is divisible by 2, then it is
even. If a number is even, then it is an integer.
Conjecture: If a number is an integer, then it is
divisible by 2.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Check It Out! Example 3
Determine if the conjecture is valid by the Law
of Syllogism.
Given: If an animal is a mammal, then it has
hair. If an animal is a dog, then it is a mammal.
Conjecture: If an animal is a dog, then it has
hair.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 4: Applying the Laws of Deductive
Reasoning
Draw a conclusion from the given information.
A. Given: If 2y = 4, then z = –1. If x + 3 = 12,
then 2y = 4. x + 3 = 12
B. If the sum of the measures of two angles is
180°, then the angles are supplementary. If two
angles are supplementary, they are not angles
of a triangle. mA= 135°, and mB= 45°.
Holt McDougal Geometry