1. 2-5: Verifying Segment Relationships
Expectations:
L4.3.1: Know the basic structure of an “If, then” proof.
G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems.
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2-5: Verifying Segment Relationships

2. Equivalence Property of Congruence Theorem
a. Congruence of segments is reflexive
AB 
b. Congruence of segments is symmetric:
If AB  CD, then
c. Congruence of segments is transitive:
If AB  CD and CD  EF, then
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2-5: Verifying Segment Relationships

3. Parts of a Geometric Proof
a. State the theorem (may already be done for you).
b. State the given (hypothesis) and what you are trying to prove (conclusion).
c. Draw a diagram.
d. Start with the given and deduce statements until you reach the conclusion.
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2-5: Verifying Segment Relationships

4. Prove the Symmetric Property of Congruence
State the theorem:
What is the given?
What must we prove?
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2-5: Verifying Segment Relationships

5. 2-5: Verifying Segment Relationships
Complete the Proof
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2-5: Verifying Segment Relationships

6. 2-5: Verifying Segment Relationships
Given: P, Q and S are collinear
Prove: PQ = PS – QS P Q S
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2-5: Verifying Segment Relationships

7. 2-5: Verifying Segment Relationships
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2-5: Verifying Segment Relationships

8. 2-5: Verifying Segment Relationships
Jerry stated that squaring a number always results in a positive result. Which of the following numbers is a counterexample to Jerry’s statement? -3
.-75 -½ 1⅓
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2-5: Verifying Segment Relationships

9. 2-5: Verifying Segment Relationships
Complete Study Guide/Practice 2-5. Finish as homework.
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2-5: Verifying Segment Relationships

10. 2-5: Verifying Segment Relationships
What is the negation of the statement, “No squares are triangles?”
all squares are triangles
all triangles are squares
no triangles are squares
there exists at least one square that is a triangle.
There exists at least one triangle that is a square.
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2-5: Verifying Segment Relationships

11. 2-5: Verifying Segment Relationships
Assignment
pages ,
# (odds), (odds).
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2-5: Verifying Segment Relationships