GEOMETRIC PROOF
Section 5.2
Essential Question: How can algebraic concepts be applied
to geometry?
Real-World Link
■ A police detective uses analytical thinking to solve crimes.
■ ___________________ reasoning is the process of making a
conjecture after observing several examples.
■ Unlike inductive reasoning, __________________ reasoning
uses facts, rules, definition, or laws to make conjectures
from given situations.
Graphic Organizer: Match each
situation with the type of reasoning
used
After performing a
Every time Bill watches his
favorite team on television, the
team loses. So, he decides to
not watch the team play on TV
All triangles have 3 sides and 3
angles. Mariah has a figure with 3
sides and 3 angles, so it must be a
triangle.
science experiment,
LaDell concluded that
only 80% of tomato seeds
would grow into plants.
In order to play sports, you need
to have a B average. Simon has
a B average, so he concludes he
can play sports.
The Proof Process
Step 1
List the given information, or
what you know. If possible,
draw a diagram to illustrate
this information
Given
Step 2
State what is to be proven
Hypothesis
Step 3
Create a deductive argument
by forming a logical chain of
statements linking the given
information to what you are
trying to prove
Statements and Reasons
Step 4
Justify each statement with a
reason. Reasons include
definitions, algebraic
properties, and theorems
Statements and Reasons
Step 5
State what it is you have
proven
Prove (Conclusion)
Notes
■ A ____________________ is a logical argument where each
statement is justified by a reason.
■ A ___________________, also called an ________________,
involves writing a paragraph to explain why a conjecture is
true.
Example on pg. 381
Two-Column Proofs
■ A _____________________ proof, or ________________
proof contains statements and reasons organized in two
columns.
■ Once a statement or conjecture has been proven, it is called
a ______________________, and it can be used as a reason
to justify statements in other proofs.
Example
NAME
Use the figure to complete the reasons in the two-column
proof to show that if linesDATE
b and
e are parallel and cut by
____________________________________________
____________________________
transversal a, then ∠1 is congruent to ∠3.
Statements
a. Lines b and c are parallel
and cut by transversal a
b. m∠1 = m∠2
c. m∠2 = m∠3
d. m∠1 = m∠3
Reasons
PERIOD ____________
Example
Given: Lines a and b are parallel and cut by transversal c; ∠1 is a right angle
Prove: b ⊥ c
Statements
a. a || b, cut by transversal c
m∠1 = 90
Reasons
________________
b. m∠1 = m∠5
________________
c. m∠5 = 90
________________
d. b ⊥ c
________________
Essential Question
■ How is deductive reasoning used in algebra and geometric
proofs?
■ __________________________________________________
__________________________________________________
__________________________________________________
__________________________________________________
________