Download Geometry A Test Out Unit 1: The Language of Geometry • I can know

Geometry A Test Out
Unit 1: The Language of Geometry
• I can know and understand the undefined terms in geometry.
• I can define and represent the geometric terms segment, line, ray, endpoint, opposite
rays, collinear, coplanar, midpoint, bisector, angle, vertex, adjacent angles, linear pair,
complementary angles, supplementary angles, and vertical angles.
• I can describe a postulate and explain the importance of postulates in geometry.
• I can explain all of the postulates discussed in Unit 1.
• I can construct a segment, congruent angle, and angle bisector.
• I can solve multi-step problems involving segments and angles.
• I can classify angles (acute, right, obtuse, and straight).
• I can classify vertical angles, adjacent angles, and linear pairs.
• I can define and represent parallel lines, perpendicular lines, skew lines, and parallel
planes.
• I can construct a perpendicular bisector, a line perpendicular to a line through a point not
on the line, a line parallel to a line through a point not on the line.
• I can determine if two segments are parallel, perpendicular, or neither on the coordinate
plane.
• I can find the midpoint of a segment in the coordinate plane using the Midpoint Formula.
• I can find the length of a segment in the coordinate plane using the Distance Formula.
Unit 2: Mathematical Reasoning
• I can understand what inductive reasoning is and its importance in geometry.
• I can recognize and write conditional statements and determine their truth value.
• I can show that a conditional is false by finding a counterexample.
• I can understand what deductive reasoning is and its importance in geometry.
• I can determine the validity of conclusions using the Law of Detachment and the Law of
Syllogism.
• I can write a definition as a biconditional.
• I can determine if a biconditional statement is true or false.
• I can write an algebra proof.
• I can justify a statement using a properties, definitions, postulates, and theorems.
• I can write a deductive proof involving lines, angles, and segments.
• I can prove the following theorems: Right Angle Congruence, Vertical Angles, and Linear
Pair.
• I can recognize angle pairs when two lines are cut by a transversal.
• I can prove and apply the following theorems: Corresponding Angles Postulate, Alternate
Interior Angles Theorem, Alternate Exterior Angles Theorem, and Same-side Interior
Angles Theorem.
• I can prove and apply the following theorems: Converse of Corresponding Angles
Postulate, Converse of Alternate Interior Angles Theorem, Converse of Alternate Exterior
Angles Theorem, and Converse of Same-side Interior Angles Theorem.
Unit 3: Transformations
• I can understand function notation for transformations.
• I can perform a coordinate transformation, given the rule.
• I can know the properties of rigid motions and recognize a transformation that is a rigid
motion.
• I can recognize the following transformations: reflection, rotation, translation, and dilation.
• I can make a drawing of a reflection, translation, rotation, and dilation.
• I can make a construction of a reflection and a translation.
• I can draw a composition of transformations.
• I can perform the following transformations in the coordinate plane: reflection over
• I can perform the following transformations in the coordinate plane: reflection over y-axis,
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x-axis, line y=x; rotation 90 degrees about the origin, rotation 180 degrees about the
origin, translation by a vector in component form, and dilation by a scale factor k.
I can recognize that a translation is a reflection over two parallel lines and that a rotation
is a reflection over two intersecting lines.
I can, given a reflection, determine where the line of reflection is.
I can, given a rotation, determine two lines of reflection that would produce an equivalent
transformation.
I can, given a translation, determine two lines of reflection that would produce an
equivalent transformation.
I can, given a dilation, determine the center of dilation and the scale factor.
Unit 4: Congruence
• I can classify a triangle by its angle measures and by its side lengths.
• I can prove and apply the following theorems: Triangle Sum, each angle in an
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equiangular triangle is 60 degrees, Exterior Angle Theorem, 3 Angle Theorem,
Isosceles Triangle Theorem, Converse of Isosceles Triangle Theorem, Equilateral
Triangle Equiangular Triangle, Equiangular Triangle Equilateral Triangle,
Perpendicular Bisector Theorem, Converse of Perpendicular Bisector Theorem, Triangle
Midsegment Theorem, Centroid Theorem
• I can determine if two figures are congruent using the definition of congruence in terms of
rigid motions.
• I can specify a series of transformations that will carry a given figure onto another.
• I can develop an argument for CPCTC based on the definition of congruence in terms of
rigid motions.
• I can determine if two figures are congruent by determining if their corresponding parts
are congruent.
• I can develop the criteria for triangle congruence (SSS, SAS, ASA)
• I can prove the other criteria for triangle congruence (AAS and HL)
• I can use the triangle congruence criteria to solve problems and to prove relationships in
geometric figures.
• I can write a coordinate proof.
• I can understand what a median is in a triangle.
• I can understand what a centroid is in a triangle.
Unit 4: Triangle Similarity (continued)
• I can express ratios in multiple formats.
• I can solve proportions.
• I can state the properties of similarity.
• I can find the similarity ratio of similar triangles.
• I can find missing sides length of similar triangles.
• I can find missing angles of similar triangles.
• I can show triangles are similar using the AA postulate.
• I can show triangles are similar using the SAS theorem.
• I can show triangles are similar using the SSS theorem.
• I can write a similarity statement.
• I can verify that triangles are similar.
• I can apply the triangle proportionality theorem.
• I can apply the converse of the triangle proportionality theorem.
• I can apply the two-transversal proportionality corollary.
• I can apply the triangle angle bisector theorem.
• I can solve real world problems using similar triangles.
• I can use the triangle inequalities theorem.