Geometry Curriculum THE FOLLOWING UNITS AND OBJECTIVES HAVE BEEN COVERED IN CLASS DURING THE SCHOOL YEAR:

Unit 1: Geometric Thinking and Vocabulary

G.1 The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include:

a) identifying the converse, inverse, and contrapositive of a conditional statement;

b) translating a short verbal argument into symbolic form; and 

c) determining the validity of a logical argument. 

 

Geometry IXL Practice:

Identify hypotheses and conclusions (G-I.1)

Counterexamples (G-I.2)

Conditionals (G-I.3)

Negations (G-I.4)

Converses, inverses, and contrapositives (G-I.5)

Biconditionals (G-I.6)

Truth tables (G-I.7)

Truth values (G-I.8)
Unit 2: Coordinate Geometry, Basic Constructions, and Equations of Circles
G.3 The student will solve problems involving symmetry and transformation. This will include:

a) investigating and using formulas for determining distance, midpoint, and slope; 

b) applying slope to verify and determine whether lines are parallel or perpendicular; 

 

Geometry IXL Practice:

Midpoint formula: find the midpoint (G-B.7)

Midpoint formula: find the endpoint (G-B.8)

Distance formula (G-B.9)

Slopes of lines (G-E.2)

Slopes of parallel and perpendicular lines (G-E.5)

G.4 The student will construct and justify the constructions of:

a) a line segment congruent to a given line segment; 

b) the perpendicular bisector of a line segment; 

e) the bisector of a given angle; 

f) an angle congruent to a given angle; 

Geometry IXL Practice:

Construct the midpoint or perpendicular bisector of a segment (G-B.10)

Construct an angle bisector (G-C.6)

Construct a congruent angle (G-C.7)

G.12 The student will solve problems involving equations of circles.

Geometry IXL Practice:

Find the center of a circle (G-V.1)

Find the radius or diameter of a circle (G-V.2)

Write equations of circles in standard form from graphs (G-V.3)

Write equations of circles in standard form using properties (G-V.4)

Graph circles from equations in standard form (G-V.7)

Unit 3: Angle Relationships with Intersecting and Parallel Lines

G.2 The student will use the relationships between angles formed by two lines intersected by a transversal to:

a) prove two or more lines are parallel; and 

b) solve problems, including practical problems, involving angles formed when parallel lines are

intersected by a transversal. 

Geometry IXL Practice:

Transversals: name angle pairs (G-D.3)

Transversals of parallel lines: find angle measures (G-D.4)

Proofs involving parallel lines I (G-D.6)

Proofs involving parallel lines II (G-D.7)

G.4 The student will construct and justify the constructions of:

c) a perpendicular to a given line from a point not on the line; 

d) a perpendicular to a given line at a given point on the line; 

g) a line parallel to a given line through a point not on the line

Geometry IXL Practice:

Construct a perpendicular line (G-D.2)

Construct a perpendicular line (G-D.2)

Construct parallel lines (G-D.5)

Unit 4: Angle Relationships in Circles

G.11 The student will solve problems, including practical problems, by applying properties of circles. This will include determining: 

a) angle measures formed by intersecting chords, secants, and/or tangents

Geometry IXL Practice:

Central angles and arc measures (G-U.2)

Inscribed angles (G-U.9)

Angles in inscribed right triangles (G-U.10)

Angles in inscribed quadrilaterals I (G-U.11)

Angles in inscribed quadrilaterals II (G-U.12)


Unit 5: Triangle Relationships

G.5 The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include:

a) ordering the sides by length, given angle measures; 

b) ordering the angles by degree measure, given side lengths; 

c) determining whether a triangle exists; and 

d) determining the range in which the length of the third side must lie.

Geometry IXL Practice:

Congruence statements and corresponding parts (G-J.1)

Solve problems involving corresponding parts (G-J.2)

Triangle Inequality Theorem (G-M.5)


Unit 6: Congruent Triangles

G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent.

Geometry IXL Practice:

SSS and SAS Theorems (G-K.1)

Proving triangles congruent by SSS and SAS (G-K.2)

ASA and AAS Theorems (G-K.3)

Proving triangles congruent by ASA and AAS (G-K.4)

SSS, SAS, ASA, and AAS Theorems (G-K.5)

SSS Theorem in the coordinate plane (G-K.6)

Proving triangles congruent by SSS, SAS, ASA, and AAS (G-K.7)

Hypotenuse-Leg Theorem (G-K.11)


Unit 7: Similar Triangles

G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar.

Geometry IXL Practice:

Identify similar figures (G-P.3)

Side lengths and angle measures in similar figures (G-P.4)

Similar triangles and indirect measurement (G-P.5)

Similarity rules for triangles (G-P.7)

Triangle Proportionality Theorem (G-P.10)

Similarity and altitudes in right triangles

Prove similarity statements (G-P.12)


Unit 8: Right Triangles and Special Right Triangles

G.8 The student will solve problems, including practical problems, involving right triangles. This will include applying:

a) the Pythagorean Theorem and its converse; 

b) properties of special right triangles; and 

c) trigonometric ratios. 

Geometry IXL Practice:

Pythagorean Theorem (G-Q.1)

Converse of the Pythagorean theorem (G-Q.2)

Pythagorean Inequality Theorems (G-Q.3)

Special right triangles (G-Q.4)

Trigonometric ratios: sin, cos, and tan (G-R.1)

Trigonometric ratios in similar right triangles (G-R.3)

Trigonometric ratios: find a side length (G-R.8)

Trigonometric ratios: find an angle measure (G-R.9)

Solve a right triangle (G-R.10)

 

 

Unit 9: Segments in Circles

G.11 The student will solve problems, including practical problems, by applying properties of circles. This will include determining:

b) lengths of segments formed by intersecting chords, secants, and/or tangents


Geometry IXL Practice:

Tangent lines (G-U.7)

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UNITS AND OBJECTIVES THAT HAVE NOT BEEN COVERED IN CLASS DURING THE SCHOOL YEAR:


Unit 10: Quadrilaterals and Polygons

G.9 The student will verify and use properties of quadrilaterals to solve problems, including practical problems


G.10 The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the:

a) sum of the interior and/or exterior angles; 

b) measure of an interior and/or exterior angle; and 

c) number of sides of a regular polygon. 


G.4 The student will construct and justify the constructions of:

h) an equilateral triangle, a square, and a regular hexagon inscribed in a circle. 



Unit 11: 2-D Figures – Area, Perimeter, and Similarity 

G.11 The student will solve problems, including practical problems, by applying properties of circles. This will include determining:

c) arc length; and 

d) area of a sector.


G.14 The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include:

a) comparing ratios between lengths, perimeters, areas, and volumes of similar figures; 

b) determining how changes in one or more dimensions of a figure affect area and/or volume of the

figure



Unit 12: 3-D Figures

G.13 The student will use surface area and volume of three-dimensional objects to solve practical problems. 


G.14 The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include:

a) comparing ratios between lengths, perimeters, areas, and volumes of similar figures; 

b) determining how changes in one or more dimensions of a figure affect area and/or volume of the 

figure; 

c) determining how changes in area and/or volume of a figure affect one or more dimensions of the 

figure; and 

d) solving problems, including practical problems, about similar geometric figures. 



Unit 13: Symmetry and Transformations

SOL G.3 The student will solve problems involving symmetry and transformation. This will include:

c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a 

point.

d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate

methods.