High School Geometry Logic & Formal Proof Exam Pack with Analytic Rubric (preview: 3 of 8 pages) · 3 pages
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Formal Geometric Proof
Comprehensive Examination & Analytic Rubric
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NAME: DATE:
Tier 1: Propositional Logic
Conditionals and Deductive Reasoning
Analyze conditional statements, write logical variations, and identify valid laws of deduction.
1. Which law justifies: 'If p -> q is true, and p is true, then q is true'?
A) Law of SyllogismB) Law of DetachmentC) Law of ContrapositionD) Transitive Property
2. Which variation of a conditional statement is always logically equivalent to the original conditional statement?
A) ContrapositiveB) ConverseC) InverseD) Biconditional
3. The statement formed by negating both the hypothesis and conclusion of p -> q is the ____.
4. A conditional statement and its converse always share the exact same truth value.
TrueFalse
5. Write the contrapositive of: 'If two lines are perpendicular, then they intersect at right angles.'
6. Match each symbolic logical form to its correct technical title:
p -> q••Converse
q -> p••Inverse
~p -> ~q••Contrapositive
~q -> ~p••Conditional
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NAME: DATE:
Tier 2: Direct Geometric Proofs
Properties of Equality and Segment Addition
Complete the two-column proof steps and justify each transition using geometric axioms.
1. Which property validates the logical statement: 'If AB = CD, then CD = AB'?
A) Reflexive PropertyB) Transitive PropertyC) Symmetric PropertyD) Substitution Property
2. If point B lies on line segment AC between A and C, then AB + BC = AC by the Segment ____ Postulate.
3. Identify the algebraic property that justifies: If 4x - 9 = 15, then 4x = 24.
4. The definition of congruent segments states that segments are congruent if and only if their lengths are equal.
TrueFalse
5. If Angle 1 and Angle 2 form a linear pair, which justification establishes that m∠1 + m∠2 = 180°?
A) Linear Pair PostulateB) Vertical Angles TheoremC) Definition of Angle BisectorD) Angle Addition Postulate
6. Match the algebraic equality property with its symbolic representation:
a = a••Transitive
If a = b and b = c, then a = c••Symmetric
If a = b, then b = a••Substitution
If a = b, then a may replace b••Reflexive
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