US MATH GEOMETRY – EDmama US

A. Points, Lines, and Planes

A.01. Define and identify points, lines, line segments, and rays.
A.02. Understand properties of planes, lines, and points (e.g., intersection).
A.03. Calculate lengths of segments on number lines.
A.04. Apply the additive property of length.
A.05. Identify and find midpoints of line segments.
A.06. Understand and apply the concept of congruent line segments.
A.07. Utilize the midpoint formula to find midpoints and endpoints.
A.08. Apply the distance formula to find distances between points.
A.09. Construct congruent segments and perpendicular bisectors.
A.10. Partition a line segment in a given ratio.
A.11. Determine distances to the origin in three dimensions.
A.12. Prove geometric theorems related to line segments and midpoints.
A.13. Solve complex problems involving multiple line segments and points.

B. Angles

B.01. Define and classify angles using vocabulary (acute, obtuse, etc.).
B.02. Measure angles using a protractor.
B.03. Identify complementary, supplementary, vertical, and adjacent angles.
B.04. Find measures of angles using relationships between angle types.
B.05. Solve for unknown angles in diagrams using algebraic equations.
B.06. Understand and construct angle bisectors.
B.07. Construct congruent angles.
B.08. Prove geometric theorems related to angle relationships.
B.09. Solve complex problems involving multiple angles and angle relationships.

C. Parallel and Perpendicular Lines

C.01. Identify parallel, intersecting, and skew lines and planes.
C.02. Construct perpendicular lines.
C.03. Identify angle pairs formed by transversals.
C.04. Find angle measures using properties of parallel lines and transversals.
C.05. Solve for unknown angles in diagrams involving parallel lines and transversals.
C.06. Construct parallel lines.
C.07. Prove theorems involving parallel lines.
C.08. Solve complex problems involving multiple parallel and perpendicular lines and transversals.

D. Lines in the Coordinate Plane

D.01. Calculate slopes of lines.
D.02. Graph linear equations.
D.03. Write equations of lines in various forms (slope-intercept, point-slope).
D.04. Determine slopes of parallel and perpendicular lines.
D.05. Write equations of parallel and perpendicular lines.
D.06. Find the distance between a point and a line.
D.07. Find the distance between two parallel lines.
D.08. Apply coordinate geometry to prove geometric theorems.
D.09. Solve complex problems involving lines and distances in the coordinate plane.

E. Logic and Reasoning

E.01. Identify hypotheses and conclusions in statements.
E.02. Use counterexamples to disprove statements.
E.03. Understand and apply conditional statements.
E.04. Formulate negations of statements.
E.05. Determine converses, inverses, and contrapositives of conditional statements.
E.06. Understand and use biconditional statements.
E.07. Construct and interpret truth tables.
E.08. Determine truth values of statements.
E.09. Apply logical reasoning to solve geometric problems and proofs.
E.10. Construct formal geometric proofs using deductive reasoning.

F. Triangles

F.01. Classify triangles by sides and angles.
F.02. Apply the Triangle Angle-Sum Theorem.
F.03. Apply the Exterior Angle Theorem and Exterior Angle Inequality.
F.04. Understand and apply congruence postulates (SSS, SAS, ASA, AAS, HL).
F.05. Write formal proofs to prove triangle congruence.
F.06. Solve problems involving congruent triangles.
F.07. Apply triangle inequalities to determine possible side lengths and angles.
F.08. Prove theorems related to isosceles and equilateral triangles.
F.09. Solve complex geometry problems involving various triangle properties.

G. Polygons

H. Congruence Transformations

I. Dilations

J. Symmetry

K. Similar Figures

K.01. Understand ratios in similar figures.
K.02. Write similarity statements.
K.03. Identify similar figures.
K.04. Find side lengths and angle measures in similar figures.
K.05. Apply similar triangles to solve indirect measurement problems.
K.06. Calculate perimeters and areas of similar figures.
K.07. Understand and apply the Angle-Angle (AA) criterion for similar triangles.
K.08. Prove similarity statements.
K.09. Solve complex problems involving similar figures.

L. Properties of Triangles

L.01. Identify and apply properties of midsegments.
L.02. Apply properties of angle bisectors, medians, altitudes, and perpendicular bisectors.
L.03. Understand angle-side relationships in triangles.
L.04. Apply the Triangle Inequality Theorem.
L.05. Construct the circumcenter, incenter, centroid, and orthocenter of triangles.
L.06. Find the centroid of a triangle using coordinates.
L.07. Prove theorems related to triangle properties.
L.08. Solve complex problems involving multiple triangle properties.

M. Quadrilaterals

N. Pythagorean Theorem

O. Right Triangle Trigonometry

P. Laws of Sines and Cosines

Q. Area and Perimeter

Q.01. Calculate perimeter of various shapes.
Q.02. Calculate areas of rectangles, squares, parallelograms, triangles, trapezoids, rhombuses, and regular polygons.
Q.03. Calculate area and perimeter in the coordinate plane.
Q.04. Calculate area and circumference of circles.
Q.05. Calculate area of compound figures and area between shapes.
Q.06. Understand the relationship between area and perimeter of similar figures.
Q.07. Apply Heron’s formula to calculate the area of a triangle.
Q.08. Solve complex problems involving area and perimeter calculations.

R. Three-Dimensional Figures

S. Surface Area and Volume

T. Measurement

U. Circles

U.01. Identify parts of a circle.
U.02. Understand and apply relationships between central angles and arc measures.
U.03. Calculate arc length and sector area.
U.04. Convert between radians and degrees.
U.05. Understand and apply properties of arcs and chords.
U.06. Understand and apply properties of tangent lines.
U.07. Understand and apply properties of inscribed angles.
U.08. Understand and apply properties of angles formed by chords, secants, and tangents.
U.09. Understand and apply properties of segments formed by chords, secants, and tangents.
U.10. Solve complex problems involving circle properties.

V. Constructions with Circles

W. Circles in the Coordinate Plane

X. Parabolas in the Coordinate Plane

Y. Probability

Y.01. Calculate theoretical and experimental probability.
Y.02. Understand outcomes of compound events.
Y.03. Identify independent and dependent events.
Y.04. Calculate probabilities of independent and dependent events.
Y.05. Apply the counting principle.
Y.06. Calculate permutations and combinations.
Y.07. Use combinations and permutations to calculate probabilities.
Y.08. Use two-way frequency tables to calculate probabilities.
Y.09. Calculate conditional probabilities.
Y.10. Understand independence and conditional probability.
Y.11. Calculate geometric probability.
Y.12. Apply the addition rule for probability.
Y.13. Solve complex problems involving probability.

Course Content

A. Points, Lines, and Planes

A.01. Define and identify points, lines, line segments, and rays.

A.02. Understand properties of planes, lines, and points (e.g., intersection).

A.03. Calculate lengths of segments on number lines.

A.04. Apply the additive property of length.

A.05. Identify and find midpoints of line segments.

A.06. Understand and apply the concept of congruent line segments.

A.07. Utilize the midpoint formula to find midpoints and endpoints.

A.08. Apply the distance formula to find distances between points.

A.09. Construct congruent segments and perpendicular bisectors.

A.10. Partition a line segment in a given ratio.

A.11. Determine distances to the origin in three dimensions.

A.12. Prove geometric theorems related to line segments and midpoints.

A.13. Solve complex problems involving multiple line segments and points.

B. Angles

B.01. Define and classify angles using vocabulary (acute, obtuse, etc.).

B.02. Measure angles using a protractor.

B.03. Identify complementary, supplementary, vertical, and adjacent angles.

B.04. Find measures of angles using relationships between angle types.

B.05. Solve for unknown angles in diagrams using algebraic equations.

B.06. Understand and construct angle bisectors.

B.07. Construct congruent angles.

B.08. Prove geometric theorems related to angle relationships.

B.09. Solve complex problems involving multiple angles and angle relationships.

C. Parallel and Perpendicular Lines

C.01. Identify parallel, intersecting, and skew lines and planes.

C.02. Construct perpendicular lines.

C.03. Identify angle pairs formed by transversals.

C.04. Find angle measures using properties of parallel lines and transversals.

C.05. Solve for unknown angles in diagrams involving parallel lines and transversals.

C.06. Construct parallel lines.

C.07. Prove theorems involving parallel lines.

C.08. Solve complex problems involving multiple parallel and perpendicular lines and transversals.

D. Lines in the Coordinate Plane

D.01. Calculate slopes of lines.

D.02. Graph linear equations.

D.03. Write equations of lines in various forms (slope-intercept, point-slope).

D.04. Determine slopes of parallel and perpendicular lines.

D.05. Write equations of parallel and perpendicular lines.

D.06. Find the distance between a point and a line.

D.07. Find the distance between two parallel lines.

D.08. Apply coordinate geometry to prove geometric theorems.

D.09. Solve complex problems involving lines and distances in the coordinate plane.

E. Logic and Reasoning

E.01. Identify hypotheses and conclusions in statements.

E.02. Use counterexamples to disprove statements.

E.03. Understand and apply conditional statements.

E.04. Formulate negations of statements.

E.05. Determine converses, inverses, and contrapositives of conditional statements.

E.06. Understand and use biconditional statements.

E.07. Construct and interpret truth tables.

E.08. Determine truth values of statements.

E.09. Apply logical reasoning to solve geometric problems and proofs.

E.10. Construct formal geometric proofs using deductive reasoning.

F. Triangles

F.01. Classify triangles by sides and angles.

F.02. Apply the Triangle Angle-Sum Theorem.

F.03. Apply the Exterior Angle Theorem and Exterior Angle Inequality.

F.04. Understand and apply congruence postulates (SSS, SAS, ASA, AAS, HL).

F.05. Write formal proofs to prove triangle congruence.

F.06. Solve problems involving congruent triangles.

F.07. Apply triangle inequalities to determine possible side lengths and angles.

F.08. Prove theorems related to isosceles and equilateral triangles.

F.09. Solve complex geometry problems involving various triangle properties.

G. Polygons

G.01. Define and classify polygons.

G.02. Find the sum of interior and exterior angles of polygons.

G.03. Apply properties of regular polygons.

G.04. Construct equilateral triangles and regular hexagons.

G.05. Construct squares.

G.06. Apply polygon theorems to solve for unknown angles and side lengths.

G.07. Solve complex problems involving various polygon properties.

H. Congruence Transformations

H.01. Classify congruence transformations (translations, reflections, rotations, glide reflections).

H.02. Perform and graph translations, reflections, and rotations.

H.03. Find coordinates of images under congruence transformations.

H.04. Write rules for congruence transformations.

H.05. Determine sequences of transformations that map one polygon onto another.

H.06. Identify transformations that carry a polygon onto itself.