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STANDARDS

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US-VA

Math

Virginia Math

Geometry: Reasoning, Lines and Transformations

G.RLT.1

The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.

G.RLT.1.a

Translate propositional statements and compound statements into symbolic form, including negations (~𝑝, read “not 𝑝”), conjunctions (𝑝 ∧ 𝑞, read “𝑝 and 𝑞”), disjunctions (𝑝 ∨ 𝑞, read “𝑝 or 𝑞”), conditionals (𝑝 → 𝑞, read “if 𝑝 then 𝑞”), and biconditionals (𝑝 ↔ 𝑞, read “𝑝 if and only if 𝑞”), including statements representing geometric relationships.
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G.RLT.1.b

Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement, and recognize the connection between a biconditional statement and a true conditional statement with a true converse, including statements representing geometric relationships.
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G.RLT.1.c

Use Venn diagrams to represent set relationships, including union, intersection, subset, and negation.
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G.RLT.1.d

Interpret Venn diagrams, including those representing contextual situations.
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G.RLT.2

The student will analyze, prove, and justify the relationships of parallel lines cut by a transversal.

G.RLT.2.a

Prove and justify angle pair relationships formed by two parallel lines and a transversal, including:

G.RLT.2.a.i

corresponding angles;
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G.RLT.2.a.ii

alternate interior angles;
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G.RLT.2.a.iii

alternate exterior angles;
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G.RLT.2.a.iv

same-side (consecutive) interior angles; and
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G.RLT.2.a.v

same-side (consecutive) exterior angles.
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G.RLT.2.b

Prove two or more lines are parallel given angle measurements expressed numerically or algebraically.

G.RLT.2.c

Solve problems by using the relationships between pairs of angles formed by the intersection of two parallel lines and a transversal.
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G.RLT.3

The student will solve problems, including contextual problems, involving symmetry and transformation.

G.RLT.3.a

Locate, count, and draw lines of symmetry given a figure, including figures in context.
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G.RLT.3.b

Determine whether a figure has point symmetry, line symmetry, both, or neither, including figures in context.
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G.RLT.3.c

Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include:

G.RLT.3.c.i

translations;

G.RLT.3.c.ii

reflections over any horizontal or vertical line or the lines 𝑦 = 𝑥 or 𝑦 = –𝑥;

G.RLT.3.c.iii

clockwise or counterclockwise rotations of 90°, 180°, 270°, or 360° on a coordinate grid where the center of rotation is limited to the origin; and
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G.RLT.3.c.iv

dilations, from a fixed point on a coordinate grid.