MATH · ETA Reviewer

Polygons, Conditional Logic & Triangle Congruence MSA Reviewer

Polygon Properties & Diagonals, Interior/Exterior Angle Relationships, Conditional Statements & Transformations, Logical Reasoning & Truth Values, and Triangle Congruence Postulates & CPCTC.

Question 1 of 30 3%

Polygon Diagonals & Problem Solving A convex pentadecagon has 15 sides. Calculate the total number of diagonals (d) that can be drawn inside this polygon:

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Calculate total diagonals (d):

(e.g., 90)

diagonals

Interior Angles & Problem Solving A regular polygon has 12 sides (dodecagon). Calculate the exact measure of a single interior angle in degrees:

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Calculate interior angle measure in degrees:

(e.g., 150)

Polygon Properties A polygon in which every interior angle measures less than or equal to 180°, ensuring that all diagonals remain inside the figure, is classified as a:

Polygon Properties Which term describes a convex polygon that is both equilateral (all sides equal) and equiangular (all angles equal)?

Polygon Diagonals Which algebraic formula accurately calculates the total number of diagonals (d) in a convex polygon with s sides?

Exterior Angles What is the sum of the exterior angles (one at each vertex) of ANY convex polygon, regardless of its number of sides?

Interior & Exterior Angles At any vertex of a convex polygon, an interior angle and its adjacent exterior angle form a linear pair. What is the sum of their measures?

Interior Angles What is the sum of the interior angles of a convex hexagon (6 sides)?

Exterior Angles If each exterior angle of a regular polygon measures 40°, how many sides does the polygon have?

Conditional Statements In the conditional statement "If two angles are vertical, then they are congruent", what is the hypothesis (p)?

Conditional Statements In the conditional statement "If two lines are parallel, then they do not intersect", what is the conclusion (q)?

If–Then Transformations Which option correctly transforms the statement "All equilateral triangles are equiangular" into an equivalent if–then statement?

Converse Which symbolic expression represents the converse of an original conditional statement p → q?

Inverse Which symbolic form represents the inverse of a conditional statement p → q?

Contrapositive Given the original conditional statement p → q, which symbolic form represents its contrapositive?

Logical Equivalence Which related statement ALWAYS shares the exact same truth value as the original conditional statement (p → q)?

Truth Values Under what single combination of truth values is a conditional statement p → q FALSE?

Reasoning Modes Arriving at a general geometry conclusion or unproven conjecture by observing specific patterns and examples is known as:

Logic Frameworks In the S.M.A.R.T. goal-setting framework used in analytical evaluation, what does the acronym stand for?

Triangle Basics What is the key distinction between similar triangles and congruent triangles?

CPCTC Principle What does the geometric acronym CPCTC stand for?

Rigid Transformations Which rigid motion transformation flips a geometric figure over a line to produce a mirror image?

Triangle Congruence Given the congruence statement ΔCAT ≅ ΔDOG, which angle directly corresponds to ∠A?

Congruence Postulates Which postulate states: "If three sides of one triangle are congruent to three corresponding sides of another triangle, then the two triangles are congruent"?

Congruence Postulates In the Side-Angle-Side (SAS) Congruence Postulate, what essential condition must be satisfied by the congruent angle?

Congruence Postulates If two angles and the INCLUDED side of one triangle are congruent to two angles and the included side of another triangle, which postulate proves congruence?

Congruence Theorems If two angles and a NON-INCLUDED side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, what rule proves congruence?

CPCTC & Problem Solving Given ΔTWO ≅ ΔPNE, if side WO measures 5 cm, calculate the exact length of corresponding side NE in centimeters:

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Calculate length of side NE (in cm):

(e.g., 5)

Triangle Congruence Algebra Given ΔRST ≅ ΔXYZ, with m∠R = 40° and m∠X = (2n + 10)°, solve for the value of n:

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Calculate value of n:

(e.g., 15)

Congruence Proofs Given triangles ΔABC and ΔDEF, if segment BA ≅ ED, ∠B ≅ ∠E, and segment BC ≅ EF, which postulate proves that ΔABC ≅ ΔDEF?

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